Abstract group data - 648.297

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 18, 'aut_gen_orders': [6, 6, 6, 6, 18], 'aut_gens': [[1, 2, 12, 108], [433, 58, 60, 108], [221, 218, 492, 540], [333, 34, 240, 108], [441, 602, 276, 540], [109, 386, 48, 108]], 'aut_group': None, 'aut_hash': 4488834822908264931, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 3888, 'aut_permdeg': 72, 'aut_perms': [42592552523603835658237493162212822377878690835023198355817560347027315588099878585274202070751185208957, 6973094132658639161081753543977034658186401790153717352811629913306509163456382336791595106651495795124, 37320079854059342553215069822202292412259847514241520405237458486931971500993695674806998862013846001118, 54789540716953076363800733498097168193683860921089265418986775376654868900588548243662715284193758303637, 11490110637790366514288010763094013808350260535275923862848385249087501694820401995476051208281735346386], 'aut_phi_ratio': 18.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 9, 2, 1], [2, 27, 2, 2], [3, 2, 1, 2], [3, 4, 1, 1], [3, 6, 1, 1], [3, 12, 1, 1], [6, 2, 1, 2], [6, 4, 1, 1], [6, 6, 1, 1], [6, 12, 1, 1], [6, 18, 2, 1], [6, 54, 2, 2], [9, 6, 3, 1], [9, 12, 3, 1], [18, 6, 3, 1], [18, 12, 3, 1], [18, 18, 6, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times C_3^4.C_3.C_2^3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 18, 'autcentquo_group': '972.429', 'autcentquo_hash': 429, 'autcentquo_nilpotent': False, 'autcentquo_order': 972, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_3^3.S_3^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 9, 2], [2, 27, 4], [3, 2, 2], [3, 4, 1], [3, 6, 1], [3, 12, 1], [6, 2, 2], [6, 4, 1], [6, 6, 1], [6, 12, 1], [6, 18, 2], [6, 54, 4], [9, 6, 3], [9, 12, 3], [18, 6, 3], [18, 12, 3], [18, 18, 6]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '324.37', 'commutator_count': 1, 'commutator_label': '81.3', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 297, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['324.37', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 9, 1, 2], [2, 27, 1, 4], [3, 2, 1, 2], [3, 4, 1, 1], [3, 6, 1, 1], [3, 12, 1, 1], [6, 2, 1, 2], [6, 4, 1, 1], [6, 6, 1, 1], [6, 12, 1, 1], [6, 18, 1, 2], [6, 54, 1, 4], [9, 6, 3, 1], [9, 12, 3, 1], [18, 6, 3, 1], [18, 12, 3, 1], [18, 18, 3, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 18144, 'exponent': 18, 'exponents_of_order': [4, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 1, 1]], 'familial': False, 'frattini_label': '9.2', 'frattini_quotient': '72.46', 'hash': 297, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 18, 'inner_gen_orders': [2, 6, 9, 3], 'inner_gens': [[1, 10, 12, 540], [5, 2, 528, 540], [1, 242, 12, 108], [217, 218, 12, 108]], 'inner_hash': 37, 'inner_nilpotent': False, 'inner_order': 324, 'inner_split': True, 'inner_tex': 'C_3^2:D_{18}', 'inner_used': [1, 2, 3], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 8], [2, 20], [4, 8], [6, 4], [12, 2]], 'label': '648.297', 'linC_count': 36, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 13, 'linQ_dim': 12, 'linQ_dim_count': 13, 'linR_count': 36, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C2*C3^2:D18', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 23, 'number_characteristic_subgroups': 23, 'number_conjugacy_classes': 42, 'number_divisions': 30, 'number_normal_subgroups': 39, 'number_subgroup_autclasses': 134, 'number_subgroup_classes': 206, 'number_subgroups': 2160, 'old_label': None, 'order': 648, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 127], [3, 26], [6, 278], [9, 54], [18, 162]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 6], 'outer_gen_pows': [0, 0], 'outer_gens': [[325, 334, 12, 540], [1, 326, 60, 540]], 'outer_group': '12.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 12, 'outer_permdeg': 7, 'outer_perms': [24, 724], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 8], [4, 2], [6, 8], [12, 4]], 'representations': {'PC': {'code': 290878033624618925006194142990401159984413, 'gens': [1, 2, 4, 6], 'pres': [7, -2, -2, -3, -3, -3, -2, -3, 141, 36, 170, 7402, 3125, 108, 1271, 22685, 11352, 124, 21174, 10597]}, 'Perm': {'d': 20, 'gens': [1446375508300801, 14231681682707160, 1, 135522408568781208, 19649121759590400, 8888760, 270407619022464000]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 10, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_3^2:D_{18}', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

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

  
  
  • id: 139761304
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 297, 'group_order': 648, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 139761315
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 297, 'group_order': 648, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 324, 'size': 1}
  • id: 139761326
    {'aut_label': '2B', 'centralizer': '9.a1.a1', 'counter': 3, 'group_counter': 297, 'group_order': 648, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 1, 'size': 9}
  • id: 139761337
    {'aut_label': '2B', 'centralizer': '9.a1.a1', 'counter': 4, 'group_counter': 297, 'group_order': 648, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 109, 'size': 9}
  • id: 139761341
    {'aut_label': '2D', 'centralizer': '27.b1.a1', 'counter': 5, 'group_counter': 297, 'group_order': 648, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 335, 'size': 27}
  • id: 139761342
    {'aut_label': '2E', 'centralizer': '27.c1.a1', 'counter': 6, 'group_counter': 297, 'group_order': 648, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 402, 'size': 27}
  • id: 139761343
    {'aut_label': '2E', 'centralizer': '27.c1.a1', 'counter': 7, 'group_counter': 297, 'group_order': 648, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 270, 'size': 27}
  • id: 139761344
    {'aut_label': '2D', 'centralizer': '27.b1.a1', 'counter': 8, 'group_counter': 297, 'group_order': 648, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 243, 'size': 27}
  • id: 139761345
    {'aut_label': '3A', 'centralizer': '2.b1.a1', 'counter': 9, 'group_counter': 297, 'group_order': 648, 'label': '3A', 'order': 3, 'powers': [9, 1], 'representative': 216, 'size': 2}
  • id: 139761305
    {'aut_label': '3B', 'centralizer': '2.a1.a1', 'counter': 10, 'group_counter': 297, 'group_order': 648, 'label': '3B', 'order': 3, 'powers': [10, 1], 'representative': 72, 'size': 2}
  • id: 139761306
    {'aut_label': '3C', 'centralizer': '4.a1.a1', 'counter': 11, 'group_counter': 297, 'group_order': 648, 'label': '3C', 'order': 3, 'powers': [11, 1], 'representative': 288, 'size': 4}
  • id: 139761307
    {'aut_label': '3D', 'centralizer': '6.g1.a1', 'counter': 12, 'group_counter': 297, 'group_order': 648, 'label': '3D', 'order': 3, 'powers': [12, 1], 'representative': 224, 'size': 6}
  • id: 139761308
    {'aut_label': '3E', 'centralizer': '12.a1.a1', 'counter': 13, 'group_counter': 297, 'group_order': 648, 'label': '3E', 'order': 3, 'powers': [13, 1], 'representative': 296, 'size': 12}
  • id: 139761309
    {'aut_label': '6A', 'centralizer': '2.b1.a1', 'counter': 14, 'group_counter': 297, 'group_order': 648, 'label': '6A', 'order': 6, 'powers': [9, 2], 'representative': 108, 'size': 2}
  • id: 139761310
    {'aut_label': '6B', 'centralizer': '2.a1.a1', 'counter': 15, 'group_counter': 297, 'group_order': 648, 'label': '6B', 'order': 6, 'powers': [10, 2], 'representative': 360, 'size': 2}
  • id: 139761311
    {'aut_label': '6C', 'centralizer': '4.a1.a1', 'counter': 16, 'group_counter': 297, 'group_order': 648, 'label': '6C', 'order': 6, 'powers': [11, 2], 'representative': 144, 'size': 4}
  • id: 139761312
    {'aut_label': '6D', 'centralizer': '6.g1.a1', 'counter': 17, 'group_counter': 297, 'group_order': 648, 'label': '6D', 'order': 6, 'powers': [12, 2], 'representative': 112, 'size': 6}
  • id: 139761313
    {'aut_label': '6E', 'centralizer': '12.a1.a1', 'counter': 18, 'group_counter': 297, 'group_order': 648, 'label': '6E', 'order': 6, 'powers': [13, 2], 'representative': 148, 'size': 12}
  • id: 139761314
    {'aut_label': '6F', 'centralizer': '18.b1.a1', 'counter': 19, 'group_counter': 297, 'group_order': 648, 'label': '6F', 'order': 6, 'powers': [10, 3], 'representative': 37, 'size': 18}
  • id: 139761316
    {'aut_label': '6F', 'centralizer': '18.b1.a1', 'counter': 20, 'group_counter': 297, 'group_order': 648, 'label': '6G', 'order': 6, 'powers': [10, 4], 'representative': 145, 'size': 18}
  • id: 139761317
    {'aut_label': '6H', 'centralizer': '54.d1.a1', 'counter': 21, 'group_counter': 297, 'group_order': 648, 'label': '6H', 'order': 6, 'powers': [9, 5], 'representative': 551, 'size': 54}
  • id: 139761318
    {'aut_label': '6I', 'centralizer': '54.h1.a1', 'counter': 22, 'group_counter': 297, 'group_order': 648, 'label': '6I', 'order': 6, 'powers': [12, 6], 'representative': 406, 'size': 54}
  • id: 139761319
    {'aut_label': '6I', 'centralizer': '54.h1.a1', 'counter': 23, 'group_counter': 297, 'group_order': 648, 'label': '6J', 'order': 6, 'powers': [12, 7], 'representative': 50, 'size': 54}
  • id: 139761320
    {'aut_label': '6H', 'centralizer': '54.d1.a1', 'counter': 24, 'group_counter': 297, 'group_order': 648, 'label': '6K', 'order': 6, 'powers': [9, 8], 'representative': 27, 'size': 54}
  • id: 139761321
    {'aut_label': '9A1', 'centralizer': '6.c1.a1', 'counter': 25, 'group_counter': 297, 'group_order': 648, 'label': '9A1', 'order': 9, 'powers': [26, 10], 'representative': 240, 'size': 6}
  • id: 139761322
    {'aut_label': '9A1', 'centralizer': '6.c1.a1', 'counter': 26, 'group_counter': 297, 'group_order': 648, 'label': '9A2', 'order': 9, 'powers': [27, 10], 'representative': 480, 'size': 6}
  • id: 139761323
    {'aut_label': '9A1', 'centralizer': '6.c1.a1', 'counter': 27, 'group_counter': 297, 'group_order': 648, 'label': '9A4', 'order': 9, 'powers': [25, 10], 'representative': 312, 'size': 6}
  • id: 139761324
    {'aut_label': '9B1', 'centralizer': '12.e1.a1', 'counter': 28, 'group_counter': 297, 'group_order': 648, 'label': '9B1', 'order': 9, 'powers': [29, 10], 'representative': 32, 'size': 12}
  • id: 139761325
    {'aut_label': '9B1', 'centralizer': '12.e1.a1', 'counter': 29, 'group_counter': 297, 'group_order': 648, 'label': '9B2', 'order': 9, 'powers': [30, 10], 'representative': 484, 'size': 12}
  • id: 139761327
    {'aut_label': '9B1', 'centralizer': '12.e1.a1', 'counter': 30, 'group_counter': 297, 'group_order': 648, 'label': '9B4', 'order': 9, 'powers': [28, 10], 'representative': 104, 'size': 12}
  • id: 139761328
    {'aut_label': '18A1', 'centralizer': '6.c1.a1', 'counter': 31, 'group_counter': 297, 'group_order': 648, 'label': '18A1', 'order': 18, 'powers': [25, 15], 'representative': 120, 'size': 6}
  • id: 139761329
    {'aut_label': '18A1', 'centralizer': '6.c1.a1', 'counter': 32, 'group_counter': 297, 'group_order': 648, 'label': '18A5', 'order': 18, 'powers': [27, 15], 'representative': 156, 'size': 6}
  • id: 139761330
    {'aut_label': '18A1', 'centralizer': '6.c1.a1', 'counter': 33, 'group_counter': 297, 'group_order': 648, 'label': '18A7', 'order': 18, 'powers': [26, 15], 'representative': 132, 'size': 6}
  • id: 139761331
    {'aut_label': '18B1', 'centralizer': '12.e1.a1', 'counter': 34, 'group_counter': 297, 'group_order': 648, 'label': '18B1', 'order': 18, 'powers': [28, 15], 'representative': 124, 'size': 12}
  • id: 139761332
    {'aut_label': '18B1', 'centralizer': '12.e1.a1', 'counter': 35, 'group_counter': 297, 'group_order': 648, 'label': '18B5', 'order': 18, 'powers': [30, 15], 'representative': 160, 'size': 12}
  • id: 139761333
    {'aut_label': '18B1', 'centralizer': '12.e1.a1', 'counter': 36, 'group_counter': 297, 'group_order': 648, 'label': '18B7', 'order': 18, 'powers': [29, 15], 'representative': 136, 'size': 12}
  • id: 139761334
    {'aut_label': '18C1', 'centralizer': '18.b1.a1', 'counter': 37, 'group_counter': 297, 'group_order': 648, 'label': '18C1', 'order': 18, 'powers': [25, 19], 'representative': 13, 'size': 18}
  • id: 139761335
    {'aut_label': '18C1', 'centralizer': '18.b1.a1', 'counter': 38, 'group_counter': 297, 'group_order': 648, 'label': '18C5', 'order': 18, 'powers': [27, 19], 'representative': 49, 'size': 18}
  • id: 139761336
    {'aut_label': '18C1', 'centralizer': '18.b1.a1', 'counter': 39, 'group_counter': 297, 'group_order': 648, 'label': '18C7', 'order': 18, 'powers': [26, 19], 'representative': 25, 'size': 18}
  • id: 139761338
    {'aut_label': '18C1', 'centralizer': '18.b1.a1', 'counter': 40, 'group_counter': 297, 'group_order': 648, 'label': '18D1', 'order': 18, 'powers': [25, 20], 'representative': 121, 'size': 18}
  • id: 139761339
    {'aut_label': '18C1', 'centralizer': '18.b1.a1', 'counter': 41, 'group_counter': 297, 'group_order': 648, 'label': '18D5', 'order': 18, 'powers': [27, 20], 'representative': 157, 'size': 18}
  • id: 139761340
    {'aut_label': '18C1', 'centralizer': '18.b1.a1', 'counter': 42, 'group_counter': 297, 'group_order': 648, 'label': '18D7', 'order': 18, 'powers': [26, 20], 'representative': 133, 'size': 18}
• gps_qchar •

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

  
  
  • id: 12767488
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12767499
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 12767510
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 12767512
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 12767513
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 12767514
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12767515
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12767516
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12767517
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, -1, -1, 2, 2, 2, -1, -1, 0, 0, 0, -1, -1, 0, 2, 2, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12767489
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12767490
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.2c', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 2, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 12767491
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 0, -2, 2, 0, 2, 2, 2, -1, -1, -2, -2, -2, 1, 1, 0, 0, 0, -1, 1, 0, 2, 2, 2, -1, -1, -1, -2, -2, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12767492
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 0, 2, -2, 0, 2, 2, 2, -1, -1, -2, -2, -2, 1, 1, 0, 0, 0, 1, -1, 0, 2, 2, 2, -1, -1, -1, -2, -2, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12767493
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, 2, -2, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 12767494
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12767495
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 0, -2, -2, 0, 2, 2, 2, -1, -1, 2, 2, 2, -1, -1, 0, 0, 0, 1, 1, 0, 2, 2, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12767501
    {'cdim': 4, 'counter': 21, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.4a', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 0, 0, 0, 0, 4, 4, 4, -2, -2, 4, 4, 4, -2, -2, 0, 0, 0, 0, 0, 0, -2, -2, -2, 1, 1, 1, -2, -2, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12767502
    {'cdim': 4, 'counter': 22, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.4b', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 0, 0, 0, 0, 4, 4, 4, -2, -2, -4, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, -2, -2, -2, 1, 1, 1, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12767496
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.2i', 'multiplicity': 3, 'nt': [9, 3], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 0, 0, 0, 0, 6, -3, -3, 6, -3, 6, -3, -3, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12767497
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.2j', 'multiplicity': 3, 'nt': [18, 13], 'qdim': 6, 'qvalues': [6, -6, -6, 6, 0, 0, 0, 0, 6, -3, -3, 6, -3, -6, 3, 3, -6, 3, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12767498
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.2k', 'multiplicity': 3, 'nt': [18, 13], 'qdim': 6, 'qvalues': [6, -6, 6, -6, 0, 0, 0, 0, 6, -3, -3, 6, -3, -6, 3, 3, -6, 3, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12767500
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.2l', 'multiplicity': 3, 'nt': [18, 13], 'qdim': 6, 'qvalues': [6, 6, -6, -6, 0, 0, 0, 0, 6, -3, -3, 6, -3, 6, -3, -3, 6, -3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12767505
    {'cdim': 6, 'counter': 25, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.6a', 'multiplicity': 1, 'nt': [9, 18], 'qdim': 6, 'qvalues': [6, 6, 0, 0, 2, 0, 0, 2, -3, 6, -3, 0, 0, -3, 6, -3, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12767506
    {'cdim': 6, 'counter': 26, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.6b', 'multiplicity': 1, 'nt': [18, 51], 'qdim': 6, 'qvalues': [6, 6, 0, 0, -2, 0, 0, -2, -3, 6, -3, 0, 0, -3, 6, -3, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12767507
    {'cdim': 6, 'counter': 27, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.6c', 'multiplicity': 1, 'nt': [18, 94], 'qdim': 6, 'qvalues': [6, -6, 0, 0, -2, 0, 0, 2, -3, 6, -3, 0, 0, 3, -6, 3, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12767508
    {'cdim': 6, 'counter': 28, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.6d', 'multiplicity': 1, 'nt': [18, 94], 'qdim': 6, 'qvalues': [6, -6, 0, 0, 2, 0, 0, -2, -3, 6, -3, 0, 0, 3, -6, 3, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12767503
    {'cdim': 4, 'counter': 23, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.4c', 'multiplicity': 3, 'nt': [18, 50], 'qdim': 12, 'qvalues': [12, 12, 0, 0, 0, 0, 0, 0, 12, -6, -6, -6, 3, 12, -6, -6, -6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12767504
    {'cdim': 4, 'counter': 24, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.4d', 'multiplicity': 3, 'nt': [36, 228], 'qdim': 12, 'qvalues': [12, -12, 0, 0, 0, 0, 0, 0, 12, -6, -6, -6, 3, -12, 6, 6, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12767509
    {'cdim': 12, 'counter': 29, 'faithful': False, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.12a', 'multiplicity': 1, 'nt': [18, 132], 'qdim': 12, 'qvalues': [12, 12, 0, 0, 0, 0, 0, 0, -6, -6, 3, 0, 0, -6, -6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12767511
    {'cdim': 12, 'counter': 30, 'faithful': True, 'group': '648.297', 'group_order': 648, 'image': None, 'label': '648.297.12b', 'multiplicity': 1, 'nt': [36, 1042], 'qdim': 12, 'qvalues': [12, -12, 0, 0, 0, 0, 0, 0, -6, -6, 3, 0, 0, 6, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

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

  
  
  • id: 29511225
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 648, 'label': '648.297.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 29511236
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.d1', 'kernel_order': 324, 'label': '648.297.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 29511247
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.c1', 'kernel_order': 324, 'label': '648.297.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 29511258
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.b1', 'kernel_order': 324, 'label': '648.297.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 29511262
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 324, 'label': '648.297.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 29511263
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 324, 'label': '648.297.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 29511264
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 324, 'label': '648.297.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 29511265
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 648, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 324, 'label': '648.297.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 29511266
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 108, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.b1.a1', 'kernel_order': 108, 'label': '648.297.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29511226
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 108, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 108, 'label': '648.297.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 29511227
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 108, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1.b1', 'kernel_order': 54, 'label': '648.297.2c', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 29511228
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 108, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.d1.b1', 'kernel_order': 54, 'label': '648.297.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29511229
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 108, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.d1.a1', 'kernel_order': 54, 'label': '648.297.2e', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29511230
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 108, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1.a1', 'kernel_order': 54, 'label': '648.297.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 29511231
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 108, 'counter': 15, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 54, 'label': '648.297.2g', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 29511232
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 108, 'counter': 16, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.a1', 'kernel_order': 54, 'label': '648.297.2h', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29511233
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 36, 'counter': 17, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '18.1', 'image_order': 18, 'indicator': 1, 'kernel': '18.a1.a1', 'kernel_order': 36, 'label': '648.297.2i1', 'nt': [9, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]]]}
  • id: 29511234
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 36, 'counter': 18, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '18.1', 'image_order': 18, 'indicator': 1, 'kernel': '18.a1.a1', 'kernel_order': 36, 'label': '648.297.2i2', 'nt': [9, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]]]}
  • id: 29511235
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 36, 'counter': 19, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '18.1', 'image_order': 18, 'indicator': 1, 'kernel': '18.a1.a1', 'kernel_order': 36, 'label': '648.297.2i3', 'nt': [9, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
  • id: 29511237
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 36, 'counter': 20, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '36.4', 'image_order': 36, 'indicator': 1, 'kernel': '36.c1.b1', 'kernel_order': 18, 'label': '648.297.2j1', 'nt': [18, 13], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 1], [-1, -1]]]}
  • id: 29511238
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 36, 'counter': 21, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '36.4', 'image_order': 36, 'indicator': 1, 'kernel': '36.c1.b1', 'kernel_order': 18, 'label': '648.297.2j2', 'nt': [18, 13], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]]]}
  • id: 29511239
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 36, 'counter': 22, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '36.4', 'image_order': 36, 'indicator': 1, 'kernel': '36.c1.b1', 'kernel_order': 18, 'label': '648.297.2j3', 'nt': [18, 13], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]]]}
  • id: 29511240
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 36, 'counter': 23, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '36.4', 'image_order': 36, 'indicator': 1, 'kernel': '36.c1.a1', 'kernel_order': 18, 'label': '648.297.2k1', 'nt': [18, 13], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[1, 1], [1, -1]]]}
  • id: 29511241
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 36, 'counter': 24, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '36.4', 'image_order': 36, 'indicator': 1, 'kernel': '36.c1.a1', 'kernel_order': 18, 'label': '648.297.2k2', 'nt': [18, 13], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]]]}
  • id: 29511242
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 36, 'counter': 25, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '36.4', 'image_order': 36, 'indicator': 1, 'kernel': '36.c1.a1', 'kernel_order': 18, 'label': '648.297.2k3', 'nt': [18, 13], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]]]}
  • id: 29511243
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 36, 'counter': 26, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '36.4', 'image_order': 36, 'indicator': 1, 'kernel': '36.b1.a1', 'kernel_order': 18, 'label': '648.297.2l1', 'nt': [18, 13], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]]]}
  • id: 29511244
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 36, 'counter': 27, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '36.4', 'image_order': 36, 'indicator': 1, 'kernel': '36.b1.a1', 'kernel_order': 18, 'label': '648.297.2l2', 'nt': [18, 13], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]]]}
  • id: 29511245
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 36, 'counter': 28, 'cyclotomic_n': 9, 'dim': 2, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '36.4', 'image_order': 36, 'indicator': 1, 'kernel': '36.b1.a1', 'kernel_order': 18, 'label': '648.297.2l3', 'nt': [18, 13], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]]]}
  • id: 29511246
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 18, 'counter': 29, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1.a1', 'kernel_order': 18, 'label': '648.297.4a', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29511248
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 18, 'counter': 30, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '72.46', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1.a1', 'kernel_order': 9, 'label': '648.297.4b', 'nt': [12, 37], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29511249
    {'center': '108.a1.a1', 'center_index': 108, 'center_order': 6, 'counter': 31, 'cyclotomic_n': 9, 'dim': 4, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '108.16', 'image_order': 108, 'indicator': 1, 'kernel': '108.a1.a1', 'kernel_order': 6, 'label': '648.297.4c1', 'nt': [18, 50], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 4], [2, -4]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29511250
    {'center': '108.a1.a1', 'center_index': 108, 'center_order': 6, 'counter': 32, 'cyclotomic_n': 9, 'dim': 4, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '108.16', 'image_order': 108, 'indicator': 1, 'kernel': '108.a1.a1', 'kernel_order': 6, 'label': '648.297.4c2', 'nt': [18, 50], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[2, 1], [2, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[2, 1], [2, -1]], [[2, 4], [2, -4]], [[2, 2], [2, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29511251
    {'center': '108.a1.a1', 'center_index': 108, 'center_order': 6, 'counter': 33, 'cyclotomic_n': 9, 'dim': 4, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '108.16', 'image_order': 108, 'indicator': 1, 'kernel': '108.a1.a1', 'kernel_order': 6, 'label': '648.297.4c3', 'nt': [18, 50], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[2, 4], [2, -4]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29511252
    {'center': '108.a1.a1', 'center_index': 108, 'center_order': 6, 'counter': 34, 'cyclotomic_n': 9, 'dim': 4, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '216.101', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1.a1', 'kernel_order': 3, 'label': '648.297.4d1', 'nt': [36, 228], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4], [2, -4]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 4], [-2, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29511253
    {'center': '108.a1.a1', 'center_index': 108, 'center_order': 6, 'counter': 35, 'cyclotomic_n': 9, 'dim': 4, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '216.101', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1.a1', 'kernel_order': 3, 'label': '648.297.4d2', 'nt': [36, 228], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[2, 1], [2, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-2, 1], [-2, -1]], [[-2, 4], [-2, -4]], [[-2, 2], [-2, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29511254
    {'center': '108.a1.a1', 'center_index': 108, 'center_order': 6, 'counter': 36, 'cyclotomic_n': 9, 'dim': 4, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '216.101', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1.a1', 'kernel_order': 3, 'label': '648.297.4d3', 'nt': [36, 228], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 4], [2, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-2, 4], [-2, -4]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29511255
    {'center': '108.b1.a1', 'center_index': 108, 'center_order': 6, 'counter': 37, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '108.17', 'image_order': 108, 'indicator': 1, 'kernel': '108.b1.a1', 'kernel_order': 6, 'label': '648.297.6a', 'nt': [9, 18], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29511256
    {'center': '108.b1.a1', 'center_index': 108, 'center_order': 6, 'counter': 38, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '108.17', 'image_order': 108, 'indicator': 1, 'kernel': '108.b1.a1', 'kernel_order': 6, 'label': '648.297.6b', 'nt': [18, 51], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29511257
    {'center': '108.b1.a1', 'center_index': 108, 'center_order': 6, 'counter': 39, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '216.102', 'image_order': 216, 'indicator': 1, 'kernel': '216.b1.a1', 'kernel_order': 3, 'label': '648.297.6c', 'nt': [18, 94], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29511259
    {'center': '108.b1.a1', 'center_index': 108, 'center_order': 6, 'counter': 40, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '216.102', 'image_order': 216, 'indicator': 1, 'kernel': '216.b1.a1', 'kernel_order': 3, 'label': '648.297.6d', 'nt': [18, 94], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29511260
    {'center': '324.a1.a1', 'center_index': 324, 'center_order': 2, 'counter': 41, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '324.37', 'image_order': 324, 'indicator': 1, 'kernel': '324.a1.a1', 'kernel_order': 2, 'label': '648.297.12a', 'nt': [18, 132], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29511261
    {'center': '324.a1.a1', 'center_index': 324, 'center_order': 2, 'counter': 42, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '648.297', 'group_counter': 297, 'group_order': 648, 'image': None, 'image_isoclass': '648.297', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1.a1', 'kernel_order': 1, 'label': '648.297.12b', 'nt': [36, 1042], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

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

  
  
  • id: 110362634
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 648, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '648.297.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.297', 'subgroup_hash': 297, 'subgroup_order': 648, 'subgroup_tex': 'C_2\\times C_3^2:D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362745
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 324, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.297.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.62', 'subgroup_hash': 62, 'subgroup_order': 324, 'subgroup_tex': 'C_2\\times C_3^2:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 324, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.297.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.75', 'subgroup_hash': 75, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362774
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 324, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.297.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.63', 'subgroup_hash': 63, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362785
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': True, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 5, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '648.297.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.37', 'subgroup_hash': 37, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362796
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': True, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 6, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '648.297.2.d1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.37', 'subgroup_hash': 37, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362807
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': True, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 7, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '648.297.2.d1.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.37', 'subgroup_hash': 37, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362818
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': True, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 8, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '648.297.2.d1.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.37', 'subgroup_hash': 37, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362829
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 108, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.101', 'subgroup_hash': 101, 'subgroup_order': 216, 'subgroup_tex': 'S_3\\times D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362635
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 108, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.3.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.172', 'subgroup_hash': 172, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362646
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 162, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.297.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['F', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '162.24', 'subgroup_hash': 24, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362657
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 162, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.297.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '162.4', 'subgroup_hash': 4, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362668
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 162, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.297.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '162.4', 'subgroup_hash': 4, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362679
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 162, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.297.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '162.17', 'subgroup_hash': 17, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:D_9', 'supersolvable': True, 'sylow': 0}
  • id: 110362690
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 162, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.297.4.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '162.17', 'subgroup_hash': 17, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:D_9', 'supersolvable': True, 'sylow': 0}
  • id: 110362701
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 162, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.297.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '162.5', 'subgroup_hash': 5, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:D_9', 'supersolvable': True, 'sylow': 0}
  • id: 110362712
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 162, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.297.4.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '162.5', 'subgroup_hash': 5, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:D_9', 'supersolvable': True, 'sylow': 0}
  • id: 110362723
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 108, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.297.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362734
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 108, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.297.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.27', 'subgroup_hash': 27, 'subgroup_order': 108, 'subgroup_tex': 'C_3:D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362746
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.24', 'subgroup_hash': 24, 'subgroup_order': 108, 'subgroup_tex': 'S_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362754
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362755
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.23', 'subgroup_hash': 23, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362756
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.23', 'subgroup_hash': 23, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362757
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362758
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.6.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.16', 'subgroup_hash': 16, 'subgroup_order': 108, 'subgroup_tex': 'S_3\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 110362759
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.6.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.16', 'subgroup_hash': 16, 'subgroup_order': 108, 'subgroup_tex': 'S_3\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 110362760
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.6.h1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.h1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.16', 'subgroup_hash': 16, 'subgroup_order': 108, 'subgroup_tex': 'S_3\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 110362761
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.6.h1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.h1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.16', 'subgroup_hash': 16, 'subgroup_order': 108, 'subgroup_tex': 'S_3\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 110362762
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.6.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362764
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.6.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362765
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.6.i1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362766
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.6.i1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362767
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 81, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '648.297.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '81.3', 'subgroup_hash': 3, 'subgroup_order': 81, 'subgroup_tex': 'C_3^2:C_9', 'supersolvable': True, 'sylow': 3}
  • id: 110362768
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.17', 'subgroup_hash': 17, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362769
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.9.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362770
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.9.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362771
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.9.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362772
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 54, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.297.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362773
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 54, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.297.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362775
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.297.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362776
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.297.12.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362777
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.297.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '54.7', 'subgroup_hash': 7, 'subgroup_order': 54, 'subgroup_tex': 'C_3:D_9', 'supersolvable': True, 'sylow': 0}
  • id: 110362778
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.297.12.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '54.7', 'subgroup_hash': 7, 'subgroup_order': 54, 'subgroup_tex': 'C_3:D_9', 'supersolvable': True, 'sylow': 0}
  • id: 110362779
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362780
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.4', 'subgroup_hash': 4, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 110362781
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.12.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.4', 'subgroup_hash': 4, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 110362782
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362783
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.12.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362784
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.3', 'subgroup_hash': 3, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 110362786
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.12.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.3', 'subgroup_hash': 3, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 110362787
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.3', 'subgroup_hash': 3, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 110362788
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.12.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.3', 'subgroup_hash': 3, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 110362789
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362790
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.12.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362791
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 36, 'counter': 55, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.297.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_9', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362792
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362793
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362794
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362795
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362797
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362798
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362799
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362800
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362801
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362802
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362803
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362804
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362805
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362806
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362808
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362809
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362810
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.p1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.p1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362811
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.p1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.p1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362812
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362813
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362814
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.q1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.q1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362815
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.q1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.q1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362816
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362817
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362819
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.r1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.r1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362820
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.r1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.r1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362821
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362822
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362823
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.s1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.s1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362824
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.18.s1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.s1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362825
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 27, 'counter': 86, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.297.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 110362826
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 27, 'counter': 87, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.297.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 110362827
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 110362828
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.27.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362830
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.27.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362831
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.27.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362832
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 18, 'counter': 92, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.297.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': ['S', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362833
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 18, 'counter': 93, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.297.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362834
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 94, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.297.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362835
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 95, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.297.36.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362836
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362837
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362838
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 98, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.297.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362839
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 99, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.297.36.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362636
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362637
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 101, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.297.36.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362638
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 102, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.297.36.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 110362639
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362640
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362641
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362642
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362643
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362644
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362645
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362647
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362648
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362649
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362650
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362651
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362652
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 110362653
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 110362654
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 110362655
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 110362656
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362658
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362659
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362660
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362661
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362662
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362663
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362664
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362665
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 110362666
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.36.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 110362667
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.54.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362669
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.54.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362670
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.54.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362671
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.54.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362672
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.54.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362673
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.54.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362674
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.54.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362675
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.54.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362676
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.54.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362677
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.54.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362678
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.54.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362680
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.54.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362681
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.54.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362682
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.54.l1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.l1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362683
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.54.l1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.l1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362684
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.54.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362685
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.54.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362686
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.54.m1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.m1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362687
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.54.m1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.m1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362688
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.54.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362689
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.54.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362691
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.54.n1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.n1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362692
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.54.n1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.n1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362693
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 9, 'counter': 152, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.297.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['Phi'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362694
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 9, 'counter': 153, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.297.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.17', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 17, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362695
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362696
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362697
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 156, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.297.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 110362698
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 157, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.297.72.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 110362699
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.72.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362700
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '648.297.81.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 2}
  • id: 110362702
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 6, 'counter': 160, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '648.297.108.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '108.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '108.16', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 16, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_9', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362703
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 6, 'counter': 161, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '648.297.108.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '108.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '108.17', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 17, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362704
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 162, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.297.108.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362705
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 2, 'counter': 163, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.297.108.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362706
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 164, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.297.108.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362707
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 165, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.297.108.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362708
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 166, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.297.108.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362709
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.108.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362710
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.108.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362711
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.108.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362713
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.108.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362714
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 171, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.297.108.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362715
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 172, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.297.108.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362716
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.108.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362717
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.108.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362718
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.108.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362719
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.108.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362720
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.108.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362721
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.108.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362722
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 179, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.297.108.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362724
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 180, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.297.108.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110362725
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.108.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362726
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.108.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362727
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.108.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362728
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.108.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362729
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.108.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362730
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.108.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362731
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.162.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362732
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.162.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362733
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.162.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362735
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.162.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362736
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.162.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362737
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.162.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362738
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.297.162.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.d1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 110362739
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 3, 'counter': 194, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '648.297.216.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '216.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.101', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 101, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_{18}', 'simple': True, 'solvable': True, 'special_labels': ['D2', 'C6'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362740
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 3, 'counter': 195, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '648.297.216.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '216.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.102', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 102, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6.S_3^2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362741
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 196, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.297.216.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362742
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 197, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.297.216.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362743
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 198, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.297.216.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 110362744
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 2, 'counter': 199, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '648.297.324.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '324.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '324.37', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 37, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 324, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:D_{18}', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110362747
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 200, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.297.324.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110362748
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 201, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.297.324.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110362749
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 202, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.297.324.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110362750
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 203, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.297.324.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110362751
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 204, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.297.324.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110362752
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 205, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.297.324.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110362753
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.297', 'ambient_counter': 297, 'ambient_order': 648, 'ambient_tex': 'C_2\\times C_3^2:D_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 1, 'counter': 206, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '648.297.648.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '648.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '648.297', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 297, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_3^2:D_{18}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', 'D3', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 110362634
    {'ambient': '648.297', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': ['648.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.d1.b1', '2.d1.c1', '2.d1.d1', '3.a1.a1', '3.b1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6409, 5087, 7967, 5581, 2692, 4950, 6277, 5086], 'generators': [1, 36, 48, 6, 216, 324, 4], 'label': '648.297.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.d1.b1', '2.d1.c1', '2.d1.d1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '324.37'}
  • id: 110362635
    {'ambient': '648.297', 'aut_centralizer_order': 3, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '432.769', 'aut_weyl_index': 9, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.d1.a1', '6.g1.a1', '6.i1.a1', '6.i1.b1', '6.i1.c1', '6.i1.d1', '9.b1.a1', '9.c1.a1', '9.d1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4559, -1, 3499, -1, 6285, -1, 4148, -1], 'generators': [1, 216, 36, 6, 324, 4], 'label': '648.297.3.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '3.b1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.b1.a1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 110362636
    {'ambient': '648.297', 'aut_centralizer_order': 324, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.m1.a1'], 'contains': ['72.g1.a1', '108.c1.a1', '108.d1.a1', '108.e1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3957, -1, 1274, -1, 7830, -1, 568, -1], 'generators': [324, 4, 252], 'label': '648.297.36.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '36.h1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110362637
    {'ambient': '648.297', 'aut_centralizer_order': 36, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.2', 'aut_weyl_index': 648, 'centralizer': '18.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '18.b1.a1', '18.p1.a1', '18.p1.b1'], 'contains': ['72.e1.a1', '108.f1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8704, -1, 9956, -1, 1021, -1, 8484, -1], 'generators': [1, 84, 36], 'label': '648.297.36.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.i1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110362638
    {'ambient': '648.297', 'aut_centralizer_order': 36, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.2', 'aut_weyl_index': 648, 'centralizer': '18.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.b1', '18.b1.a1', '18.p1.c1', '18.p1.d1'], 'contains': ['72.e1.a1', '108.f1.b1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8704, -1, 9475, -1, 1021, -1, 8236, -1], 'generators': [109, 84, 36], 'label': '648.297.36.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.i1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110362639
    {'ambient': '648.297', 'aut_centralizer_order': 54, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '36.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.f1.a1', '18.c1.a1', '18.q1.a1', '18.q1.b1'], 'contains': ['72.a1.a1', '108.f1.a1', '108.g1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6198, -1, 8278, -1, 3115, -1, 6852, -1], 'generators': [1, 36, 216], 'label': '648.297.36.j1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.j1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110362640
    {'ambient': '648.297', 'aut_centralizer_order': 54, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '36.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.b1', '12.f1.b1', '18.c1.a1', '18.q1.c1', '18.q1.d1'], 'contains': ['72.a1.a1', '108.f1.b1', '108.g1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6198, -1, 7411, -1, 3115, -1, 6173, -1], 'generators': [109, 36, 216], 'label': '648.297.36.j1.b1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.j1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110362641
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '18.d1.a1', '18.r1.a1', '18.r1.b1'], 'contains': ['72.d1.a1', '108.f1.a1', '108.h1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [212, -1, 4899, -1, 7185, -1, 4583, -1], 'generators': [1, 36, 4], 'label': '648.297.36.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.k1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110362642
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.b1', '18.d1.a1', '18.r1.c1', '18.r1.d1'], 'contains': ['72.d1.a1', '108.f1.b1', '108.h1.b1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [212, -1, 2579, -1, 7185, -1, 4083, -1], 'generators': [109, 36, 4], 'label': '648.297.36.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.k1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110362643
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.h1.a1', '12.i1.a1', '18.e1.a1', '18.q1.a1', '18.q1.c1'], 'contains': ['72.a1.a1', '108.i1.a1', '108.j1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7554, -1, 5755, -1, 4024, -1, 7248, -1], 'generators': [327, 216, 36], 'label': '648.297.36.l1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.l1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110362644
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.b1', '12.h1.b1', '12.i1.b1', '18.e1.a1', '18.q1.b1', '18.q1.d1'], 'contains': ['72.a1.a1', '108.i1.b1', '108.j1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7554, -1, 5497, -1, 4024, -1, 7439, -1], 'generators': [3, 216, 36], 'label': '648.297.36.l1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.l1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110362645
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '18.f1.a1', '18.s1.a1', '18.s1.c1'], 'contains': ['72.b1.a1', '108.i1.a1', '108.k1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5157, -1, 2835, -1, 8739, -1, 2296, -1], 'generators': [327, 216, 4], 'label': '648.297.36.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '36.m1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.m1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110362646
    {'ambient': '648.297', 'aut_centralizer_order': 36, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '108.38', 'aut_weyl_index': 36, 'centralizer': '36.a1.a1', 'complements': ['162.d1.b1', '162.d1.c1', '162.d1.a1', '162.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.e1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6788, 3918, 8232, 1351, 2866, 3967, 6244, 5086], 'generators': [324, 216, 4, 84, 36], 'label': '648.297.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '12.a1.a1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '324.37', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362647
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.b1', '18.f1.a1', '18.s1.b1', '18.s1.d1'], 'contains': ['72.b1.a1', '108.i1.b1', '108.k1.b1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5157, -1, 1742, -1, 8739, -1, 2487, -1], 'generators': [3, 216, 4], 'label': '648.297.36.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '36.m1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.m1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110362648
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '18.g1.a1'], 'contains': ['72.c1.a1', '108.i1.a1', '108.l1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5678, -1, 1485, -1, 9708, -1, 5226, -1], 'generators': [327, 216, 40], 'label': '648.297.36.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1.a1', 'old_label': '36.n1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362649
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.b1', '18.g1.a1'], 'contains': ['72.c1.a1', '108.i1.b1', '108.l1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5678, -1, 229, -1, 9708, -1, 5417, -1], 'generators': [3, 216, 40], 'label': '648.297.36.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1.a1', 'old_label': '36.n1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362650
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 108, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '18.h1.a1', '18.r1.a1', '18.r1.c1'], 'contains': ['72.d1.a1', '108.j1.a1', '108.k1.a1', '108.l1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1570, -1, 365, -1, 8991, -1, 4743, -1], 'generators': [327, 4, 36], 'label': '648.297.36.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.o1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.o1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362651
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 108, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.b1', '18.h1.a1', '18.r1.b1', '18.r1.d1'], 'contains': ['72.d1.a1', '108.j1.b1', '108.k1.b1', '108.l1.b1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1570, -1, 44, -1, 8991, -1, 5066, -1], 'generators': [3, 4, 36], 'label': '648.297.36.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.o1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.o1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362652
    {'ambient': '648.297', 'aut_centralizer_order': 12, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '54.6', 'aut_weyl_index': 72, 'centralizer': '54.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '18.i1.a1', '18.p1.a1', '18.p1.c1'], 'contains': ['72.e1.a1', '108.j1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9283, -1, 8508, -1, 1395, -1, 8598, -1], 'generators': [327, 480, 36], 'label': '648.297.36.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.p1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1.a1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 110362653
    {'ambient': '648.297', 'aut_centralizer_order': 12, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '54.6', 'aut_weyl_index': 72, 'centralizer': '54.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.b1', '18.i1.a1', '18.p1.b1', '18.p1.d1'], 'contains': ['72.e1.a1', '108.j1.b1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9283, -1, 7996, -1, 1395, -1, 8700, -1], 'generators': [3, 480, 36], 'label': '648.297.36.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.p1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1.b1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 110362654
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '54.6', 'aut_weyl_index': 72, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '18.j1.a1'], 'contains': ['72.f1.a1', '108.j1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9133, -1, 7756, -1, 2358, -1, 9596, -1], 'generators': [327, 52, 36], 'label': '648.297.36.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '36.q1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.q1.a1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 110362655
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '54.6', 'aut_weyl_index': 72, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.b1', '18.j1.a1'], 'contains': ['72.f1.a1', '108.j1.b1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9133, -1, 7604, -1, 2358, -1, 9745, -1], 'generators': [3, 52, 36], 'label': '648.297.36.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '36.q1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.q1.b1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 110362656
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '18.k1.a1', '18.s1.a1', '18.s1.d1'], 'contains': ['72.b1.a1', '108.m1.a1', '108.n1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2158, -1, 3138, -1, 5612, -1, 953, -1], 'generators': [114, 4, 216], 'label': '648.297.36.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '36.r1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.r1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110362657
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '324.117', 'aut_weyl_index': 12, 'centralizer': '108.b1.a1', 'complements': ['162.c1.a1', '162.b1.a1', '162.d1.c1', '162.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.d1.b1'], 'contains': ['8.a1.a1', '12.c1.a1', '12.f1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5940, 8035, 8903, 8103, 2520, 7464, 6463, 1785], 'generators': [1, 216, 84, 36, 4], 'label': '648.297.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.a1', '2.d1.b1'], 'normal_contains': ['8.a1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '648.297', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 110362658
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.b1', '18.k1.a1', '18.s1.b1', '18.s1.c1'], 'contains': ['72.b1.a1', '108.m1.b1', '108.n1.b1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2158, -1, 4044, -1, 5612, -1, 1144, -1], 'generators': [6, 4, 216], 'label': '648.297.36.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '36.r1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.r1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110362659
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '18.l1.a1', '18.r1.a1', '18.r1.d1'], 'contains': ['72.d1.a1', '108.m1.a1', '108.o1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [654, -1, 714, -1, 5913, -1, 3701, -1], 'generators': [114, 4, 36], 'label': '648.297.36.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.s1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.s1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110362660
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.b1', '18.l1.a1', '18.r1.b1', '18.r1.c1'], 'contains': ['72.d1.a1', '108.m1.b1', '108.o1.b1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [654, -1, 3716, -1, 5913, -1, 3892, -1], 'generators': [6, 4, 36], 'label': '648.297.36.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.s1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.s1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110362661
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '18.m1.a1'], 'contains': ['72.g1.a1', '108.m1.a1', '108.p1.a1'], 'core': '648.a1.a1', 'coset_action_label': '36T1042', 'count': 18, 'diagramx': [3674, -1, 1110, -1, 5311, -1, 83, -1], 'generators': [114, 4, 252], 'label': '648.297.36.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1.a1', 'old_label': '36.t1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.t1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362662
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.b1', '18.m1.a1'], 'contains': ['72.g1.a1', '108.m1.b1', '108.p1.b1'], 'core': '648.a1.a1', 'coset_action_label': '36T1042', 'count': 18, 'diagramx': [3674, -1, 3880, -1, 5311, -1, 274, -1], 'generators': [6, 4, 252], 'label': '648.297.36.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1.a1', 'old_label': '36.t1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.t1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362663
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 108, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.j1.a1', '18.n1.a1', '18.q1.a1', '18.q1.d1'], 'contains': ['72.a1.a1', '108.n1.a1', '108.o1.a1', '108.p1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6515, -1, 6051, -1, 2540, -1, 5680, -1], 'generators': [114, 36, 216], 'label': '648.297.36.u1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.u1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.u1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362664
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 108, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '12.j1.b1', '18.n1.a1', '18.q1.b1', '18.q1.c1'], 'contains': ['72.a1.a1', '108.n1.b1', '108.o1.b1', '108.p1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6515, -1, 8141, -1, 2540, -1, 5808, -1], 'generators': [6, 36, 216], 'label': '648.297.36.u1.b1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.u1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.u1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362665
    {'ambient': '648.297', 'aut_centralizer_order': 4, 'aut_label': '36.v1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '54.6', 'aut_weyl_index': 72, 'centralizer': '162.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '18.o1.a1', '18.p1.a1', '18.p1.d1'], 'contains': ['72.e1.a1', '108.o1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9433, -1, 8750, -1, 843, -1, 8021, -1], 'generators': [114, 48, 36], 'label': '648.297.36.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.v1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.v1.a1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 110362666
    {'ambient': '648.297', 'aut_centralizer_order': 4, 'aut_label': '36.v1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '54.6', 'aut_weyl_index': 72, 'centralizer': '162.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '18.o1.a1', '18.p1.b1', '18.p1.c1'], 'contains': ['72.e1.a1', '108.o1.b1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9433, -1, 9859, -1, 843, -1, 8122, -1], 'generators': [6, 48, 36], 'label': '648.297.36.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.v1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.v1.b1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 110362667
    {'ambient': '648.297', 'aut_centralizer_order': 108, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 972, 'centralizer': '18.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '18.c1.a1', '18.d1.a1', '27.a1.a1'], 'contains': ['108.b1.a1', '108.f1.a1', '108.f1.b1', '162.a1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6565, -1, 7558, -1, 3418, -1, 6660, -1], 'generators': [1, 324, 36], 'label': '648.297.54.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.a1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110362668
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '324.117', 'aut_weyl_index': 12, 'centralizer': '108.b1.a1', 'complements': ['162.c1.a1', '162.b1.a1', '162.d1.b1', '162.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.c1', '2.d1.d1'], 'contains': ['8.a1.a1', '12.c1.b1', '12.f1.b1'], 'core': '4.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5940, 8035, 8512, 9194, 2520, 7464, 6025, 2674], 'generators': [109, 216, 84, 36, 4], 'label': '648.297.4.b1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.b1', 'normal_contained_in': ['2.a1.a1', '2.d1.c1', '2.d1.d1'], 'normal_contains': ['8.a1.a1', '12.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.b1', 'projective_image': '648.297', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.b1.b1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 110362669
    {'ambient': '648.297', 'aut_centralizer_order': 108, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '18.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.c1.a1', '27.b1.a1'], 'contains': ['108.a1.a1', '108.g1.a1', '108.g1.b1', '162.a1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3778, -1, 5255, -1, 5080, -1, 3158, -1], 'generators': [1, 324, 216], 'label': '648.297.54.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '54.b1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362670
    {'ambient': '648.297', 'aut_centralizer_order': 36, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '54.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.d1.a1', '27.c1.a1'], 'contains': ['108.d1.a1', '108.h1.a1', '108.h1.b1', '162.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [56, -1, 2894, -1, 7416, -1, 1624, -1], 'generators': [1, 324, 4], 'label': '648.297.54.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '54.c1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362671
    {'ambient': '648.297', 'aut_centralizer_order': 36, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 972, 'centralizer': '54.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1.a1', '18.f1.a1', '18.g1.a1', '27.b1.a1'], 'contains': ['108.a1.a1', '108.i1.a1', '108.i1.b1', '162.b1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [5473, -1, 2588, -1, 6519, -1, 3508, -1], 'generators': [3, 324, 216], 'label': '648.297.54.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '54.d1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110362672
    {'ambient': '648.297', 'aut_centralizer_order': 36, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '54.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1.a1', '18.h1.a1', '18.i1.a1', '18.j1.a1', '27.a1.a1'], 'contains': ['108.b1.a1', '108.j1.a1', '108.j1.b1', '162.b1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8110, -1, 5575, -1, 4256, -1, 7586, -1], 'generators': [3, 324, 36], 'label': '648.297.54.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '54.e1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362673
    {'ambient': '648.297', 'aut_centralizer_order': 36, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '54.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1.a1', '18.h1.a1', '27.c1.a1'], 'contains': ['108.d1.a1', '108.k1.a1', '108.k1.b1', '162.b1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1896, -1, 1157, -1, 9174, -1, 2634, -1], 'generators': [3, 324, 4], 'label': '648.297.54.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '54.f1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362674
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1.a1', '18.h1.a1'], 'contains': ['108.e1.a1', '108.l1.a1', '108.l1.b1', '162.b1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3628, -1, 361, -1, 9940, -1, 5564, -1], 'generators': [3, 324, 40], 'label': '648.297.54.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1.a1', 'old_label': '54.g1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362675
    {'ambient': '648.297', 'aut_centralizer_order': 36, 'aut_label': '54.h1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 972, 'centralizer': '54.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.k1.a1', '18.l1.a1', '18.m1.a1', '27.c1.a1'], 'contains': ['108.d1.a1', '108.m1.a1', '108.m1.b1', '162.c1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1599, -1, 2055, -1, 6216, -1, 760, -1], 'generators': [6, 324, 4], 'label': '648.297.54.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1.a1', 'old_label': '54.h1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110362676
    {'ambient': '648.297', 'aut_centralizer_order': 36, 'aut_label': '54.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '54.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.k1.a1', '18.n1.a1', '27.b1.a1'], 'contains': ['108.a1.a1', '108.n1.a1', '108.n1.b1', '162.c1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4386, -1, 4695, -1, 4576, -1, 2736, -1], 'generators': [6, 324, 216], 'label': '648.297.54.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '54.i1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362677
    {'ambient': '648.297', 'aut_centralizer_order': 36, 'aut_label': '54.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '54.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.l1.a1', '18.n1.a1', '18.o1.a1', '27.a1.a1'], 'contains': ['108.b1.a1', '108.o1.a1', '108.o1.b1', '162.c1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6931, -1, 7114, -1, 2723, -1, 5924, -1], 'generators': [6, 324, 36], 'label': '648.297.54.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '54.j1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362678
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '54.k1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.a1', '18.n1.a1'], 'contains': ['108.c1.a1', '108.p1.a1', '108.p1.b1', '162.c1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5859, -1, 5965, -1, 4416, -1, 421, -1], 'generators': [6, 324, 252], 'label': '648.297.54.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1.a1', 'old_label': '54.k1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362679
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '324.118', 'aut_weyl_index': 12, 'centralizer': '108.a1.a1', 'complements': ['162.c1.a1', '162.a1.a1', '162.d1.b1', '162.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.d1.c1'], 'contains': ['8.a1.a1', '12.g1.a1', '12.h1.a1', '12.i1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6330, 6182, 7429, 4088, 3271, 5890, 6910, 3760], 'generators': [327, 216, 4, 480, 36], 'label': '648.297.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.d1.c1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '648.297', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '108.16'}
  • id: 110362680
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '54.l1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '162.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.p1.a1', '18.q1.a1', '18.r1.a1', '27.a1.a1'], 'contains': ['108.f1.a1', '108.j1.a1', '108.o1.a1', '162.d1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [6781, -1, 6751, -1, 2883, -1, 6999, -1], 'generators': [433, 114, 36], 'label': '648.297.54.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.l1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.l1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362681
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '54.l1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '162.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.p1.b1', '18.q1.b1', '18.r1.b1', '27.a1.a1'], 'contains': ['108.f1.a1', '108.j1.b1', '108.o1.b1', '162.d1.b1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [6781, -1, 8328, -1, 2883, -1, 7101, -1], 'generators': [1, 6, 36], 'label': '648.297.54.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.l1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.l1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362682
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '54.l1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '162.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.p1.c1', '18.q1.c1', '18.r1.c1', '27.a1.a1'], 'contains': ['108.f1.b1', '108.j1.a1', '108.o1.b1', '162.d1.c1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [6781, -1, 7386, -1, 2883, -1, 6320, -1], 'generators': [325, 6, 36], 'label': '648.297.54.l1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.l1.c1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.l1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362808
    {'ambient': '648.297', 'aut_centralizer_order': 2, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '54.6', 'aut_weyl_index': 72, 'centralizer': '162.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '9.a1.a1'], 'contains': ['36.i1.a1', '36.p1.a1', '36.v1.a1', '54.l1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8966, -1, 8610, -1, 277, -1, 8954, -1], 'generators': [433, 114, 48, 36], 'label': '648.297.18.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.p1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.p1.a1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 110362683
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '54.l1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '162.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.p1.d1', '18.q1.d1', '18.r1.d1', '27.a1.a1'], 'contains': ['108.f1.b1', '108.j1.b1', '108.o1.a1', '162.d1.d1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [6781, -1, 5663, -1, 2883, -1, 6026, -1], 'generators': [109, 114, 36], 'label': '648.297.54.l1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.l1.d1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.l1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362684
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '54.m1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '162.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.q1.a1', '18.s1.a1', '27.b1.a1'], 'contains': ['108.g1.a1', '108.i1.a1', '108.n1.a1', '162.d1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4007, -1, 4196, -1, 4737, -1, 3260, -1], 'generators': [1, 114, 216], 'label': '648.297.54.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '54.m1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.m1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362685
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '54.m1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '162.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.q1.b1', '18.s1.b1', '27.b1.a1'], 'contains': ['108.g1.a1', '108.i1.b1', '108.n1.b1', '162.d1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4007, -1, 6211, -1, 4737, -1, 3361, -1], 'generators': [1, 6, 216], 'label': '648.297.54.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '54.m1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.m1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362686
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '54.m1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '162.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.q1.c1', '18.s1.c1', '27.b1.a1'], 'contains': ['108.g1.b1', '108.i1.a1', '108.n1.b1', '162.d1.c1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4007, -1, 5038, -1, 4737, -1, 2940, -1], 'generators': [109, 6, 216], 'label': '648.297.54.m1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '54.m1.c1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.m1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362687
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '54.m1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '162.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.q1.d1', '18.s1.d1', '27.b1.a1'], 'contains': ['108.g1.b1', '108.i1.b1', '108.n1.a1', '162.d1.d1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4007, -1, 3791, -1, 4737, -1, 2838, -1], 'generators': [109, 114, 216], 'label': '648.297.54.m1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '54.m1.d1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.m1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362688
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '54.n1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '162.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.r1.a1', '18.s1.a1', '27.c1.a1'], 'contains': ['108.h1.a1', '108.k1.a1', '108.m1.a1', '162.d1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [494, -1, 1837, -1, 6750, -1, 1919, -1], 'generators': [433, 114, 4], 'label': '648.297.54.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1.a1', 'old_label': '54.n1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.n1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362689
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '54.n1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '162.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.r1.b1', '18.s1.b1', '27.c1.a1'], 'contains': ['108.h1.a1', '108.k1.b1', '108.m1.b1', '162.d1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [494, -1, 3971, -1, 6750, -1, 2020, -1], 'generators': [1, 6, 4], 'label': '648.297.54.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1.a1', 'old_label': '54.n1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.n1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362690
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '324.118', 'aut_weyl_index': 12, 'centralizer': '108.a1.a1', 'complements': ['162.c1.a1', '162.a1.a1', '162.d1.c1', '162.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.b1', '2.d1.d1'], 'contains': ['8.a1.a1', '12.g1.b1', '12.h1.b1', '12.i1.b1'], 'core': '4.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6330, 6182, 7170, 6771, 3271, 5890, 7159, 6412], 'generators': [3, 216, 4, 480, 36], 'label': '648.297.4.c1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.b1', 'normal_contained_in': ['2.b1.a1', '2.d1.b1', '2.d1.d1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.b1', 'projective_image': '648.297', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.c1.b1', 'subgroup_fusion': None, 'weyl_group': '108.16'}
  • id: 110362691
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '54.n1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '162.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.r1.c1', '18.s1.c1', '27.c1.a1'], 'contains': ['108.h1.b1', '108.k1.a1', '108.m1.b1', '162.d1.c1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [494, -1, 2760, -1, 6750, -1, 1393, -1], 'generators': [325, 6, 4], 'label': '648.297.54.n1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1.a1', 'old_label': '54.n1.c1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.n1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362692
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '54.n1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '162.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.r1.d1', '18.s1.d1', '27.c1.a1'], 'contains': ['108.h1.b1', '108.k1.b1', '108.m1.a1', '162.d1.d1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [494, -1, 1704, -1, 6750, -1, 1291, -1], 'generators': [109, 114, 4], 'label': '648.297.54.n1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1.a1', 'old_label': '54.n1.d1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.n1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362693
    {'ambient': '648.297', 'aut_centralizer_order': 972, 'aut_label': '72.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 972, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.b1.a1', '24.c1.a1', '36.a1.a1', '36.j1.a1', '36.j1.b1', '36.l1.a1', '36.l1.b1', '36.u1.a1', '36.u1.b1'], 'contains': ['216.a1.a1', '216.b1.a1', '216.c1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7475, 3806, 7847, 4865, 3549, 5203, 6412, 4364], 'generators': [36, 216], 'label': '648.297.72.a1.a1', 'mobius_quo': 1, 'mobius_sub': -72, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['24.a1.a1', '24.b1.a1', '36.a1.a1'], 'normal_contains': ['216.b1.a1', '216.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '648.297', 'quotient_action_image': '4.2', 'quotient_action_kernel': '18.5', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110362694
    {'ambient': '648.297', 'aut_centralizer_order': 324, 'aut_label': '72.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '12.a1.a1', 'complements': ['9.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.b1.a1', '36.c1.a1', '36.c1.b1', '36.m1.a1', '36.m1.b1', '36.r1.a1', '36.r1.b1'], 'contains': ['216.a1.a1', '216.d1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2768, 6680, 3262, 6663, 7347, 6830, 2028, 3242], 'generators': [4, 216], 'label': '648.297.72.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.b1.a1', 'normal_contained_in': ['24.a1.a1', '36.b1.a1', '36.c1.a1', '36.c1.b1'], 'normal_contains': ['216.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.b1.a1', 'projective_image': '648.297', 'quotient_action_image': '12.4', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110362695
    {'ambient': '648.297', 'aut_centralizer_order': 324, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.d1.a1', '36.n1.a1', '36.n1.b1'], 'contains': ['216.a1.a1', '216.e1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4692, -1, 2287, -1, 8033, -1, 4568, -1], 'generators': [40, 216], 'label': '648.297.72.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '72.c1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362696
    {'ambient': '648.297', 'aut_centralizer_order': 324, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 972, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.e1.a1', '36.k1.a1', '36.k1.b1', '36.o1.a1', '36.o1.b1', '36.s1.a1', '36.s1.b1'], 'contains': ['216.b1.a1', '216.d1.a1', '216.e1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1252, -1, 799, -1, 7530, -1, 4337, -1], 'generators': [4, 36], 'label': '648.297.72.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.d1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110362697
    {'ambient': '648.297', 'aut_centralizer_order': 216, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.2', 'aut_weyl_index': 648, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '36.f1.a1', '36.i1.a1', '36.i1.b1', '36.p1.a1', '36.p1.b1', '36.v1.a1', '36.v1.b1'], 'contains': ['216.b1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8900, -1, 9475, -1, 1306, -1, 8236, -1], 'generators': [84], 'label': '648.297.72.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.e1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110362698
    {'ambient': '648.297', 'aut_centralizer_order': 108, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 648, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '36.g1.a1', '36.q1.a1', '36.q1.b1'], 'contains': ['216.b1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8431, -1, 8052, -1, 2269, -1, 9483, -1], 'generators': [88], 'label': '648.297.72.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '72.f1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110362699
    {'ambient': '648.297', 'aut_centralizer_order': 324, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.h1.a1', '36.t1.a1', '36.t1.b1'], 'contains': ['216.c1.a1', '216.d1.a1', '216.e1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3176, -1, 1589, -1, 7165, -1, 1199, -1], 'generators': [4, 252], 'label': '648.297.72.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '72.g1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110362700
    {'ambient': '648.297', 'aut_centralizer_order': 12, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '4.2', 'aut_weyl_index': 972, 'centralizer': '81.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1.a1', '27.b1.a1', '27.c1.a1'], 'contains': ['162.a1.a1', '162.b1.a1', '162.c1.a1', '162.d1.a1', '162.d1.b1', '162.d1.c1', '162.d1.d1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [5009, -1, 3354, -1, 4908, -1, 3049, -1], 'generators': [1, 6, 324], 'label': '648.297.81.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '81.a1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110362701
    {'ambient': '648.297', 'aut_centralizer_order': 2, 'aut_label': '4.d1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '972.429', 'aut_weyl_index': 4, 'centralizer': '324.a1.a1', 'complements': ['162.a1.a1', '162.b1.a1', '162.d1.b1', '162.d1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.d1.d1'], 'contains': ['8.a1.a1', '12.d1.a1', '12.j1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5684, 1977, 7722, 5429, 2246, 2319, 5677, 8401], 'generators': [114, 36, 4, 48, 216], 'label': '648.297.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.d1.d1'], 'normal_contains': ['8.a1.a1', '12.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '648.297', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '324.37'}
  • id: 110362702
    {'ambient': '648.297', 'aut_centralizer_order': 1944, 'aut_label': '108.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.b1.a1', '36.d1.a1', '54.b1.a1', '54.d1.a1', '54.i1.a1'], 'contains': ['216.a1.a1', '324.a1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4453, 5895, 4552, 5170, 5525, 6017, 3267, 3803], 'generators': [324, 216], 'label': '648.297.108.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '108.a1.a1', 'normal_contained_in': ['36.a1.a1', '36.b1.a1'], 'normal_contains': ['216.a1.a1', '324.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '108.a1.a1', 'projective_image': '324.37', 'quotient_action_image': '2.1', 'quotient_action_kernel': '54.7', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '108.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110362703
    {'ambient': '648.297', 'aut_centralizer_order': 1944, 'aut_label': '108.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.e1.a1', '36.f1.a1', '36.g1.a1', '54.a1.a1', '54.e1.a1', '54.j1.a1'], 'contains': ['216.b1.a1', '324.a1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7746, 4527, 7369, 4186, 3721, 4390, 6521, 4925], 'generators': [324, 36], 'label': '648.297.108.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '108.b1.a1', 'normal_contained_in': ['36.a1.a1'], 'normal_contains': ['216.b1.a1', '324.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '108.b1.a1', 'projective_image': '324.37', 'quotient_action_image': '2.1', 'quotient_action_kernel': '54.5', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '108.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110362704
    {'ambient': '648.297', 'aut_centralizer_order': 972, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.h1.a1', '54.k1.a1'], 'contains': ['216.c1.a1', '324.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5847, -1, 5706, -1, 4496, -1, 1511, -1], 'generators': [324, 252], 'label': '648.297.108.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '108.c1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110362705
    {'ambient': '648.297', 'aut_centralizer_order': 648, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '6.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.e1.a1', '36.h1.a1', '54.c1.a1', '54.f1.a1', '54.h1.a1'], 'contains': ['216.d1.a1', '324.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1782, -1, 1833, -1, 7701, -1, 1919, -1], 'generators': [324, 4], 'label': '648.297.108.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '108.d1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110362706
    {'ambient': '648.297', 'aut_centralizer_order': 324, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '36.e1.a1', '36.h1.a1', '54.g1.a1'], 'contains': ['216.e1.a1', '324.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3289, -1, 819, -1, 8321, -1, 4446, -1], 'generators': [324, 40], 'label': '648.297.108.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '108.e1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110362707
    {'ambient': '648.297', 'aut_centralizer_order': 108, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '18.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.i1.a1', '36.j1.a1', '36.k1.a1', '54.a1.a1', '54.l1.a1', '54.l1.b1'], 'contains': ['216.b1.a1', '324.b1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6436, -1, 8416, -1, 3378, -1, 6756, -1], 'generators': [1, 36], 'label': '648.297.108.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.f1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110362708
    {'ambient': '648.297', 'aut_centralizer_order': 108, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '18.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.i1.b1', '36.j1.b1', '36.k1.b1', '54.a1.a1', '54.l1.c1', '54.l1.d1'], 'contains': ['216.b1.a1', '324.b1.b1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6436, -1, 7589, -1, 3378, -1, 6213, -1], 'generators': [109, 36], 'label': '648.297.108.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.f1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.f1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110362709
    {'ambient': '648.297', 'aut_centralizer_order': 108, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '18.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '36.j1.a1', '54.b1.a1', '54.m1.a1', '54.m1.b1'], 'contains': ['216.a1.a1', '324.b1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3845, -1, 5913, -1, 5182, -1, 3600, -1], 'generators': [1, 216], 'label': '648.297.108.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '108.g1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362710
    {'ambient': '648.297', 'aut_centralizer_order': 108, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '18.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.b1', '36.j1.b1', '54.b1.a1', '54.m1.c1', '54.m1.d1'], 'contains': ['216.a1.a1', '324.b1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3845, -1, 4921, -1, 5182, -1, 3049, -1], 'generators': [109, 216], 'label': '648.297.108.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '108.g1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.g1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362711
    {'ambient': '648.297', 'aut_centralizer_order': 36, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '54.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '36.k1.a1', '54.c1.a1', '54.n1.a1', '54.n1.b1'], 'contains': ['216.d1.a1', '324.b1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [511, -1, 4097, -1, 6962, -1, 2136, -1], 'generators': [1, 4], 'label': '648.297.108.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '108.h1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362712
    {'ambient': '648.297', 'aut_centralizer_order': 2, 'aut_label': '4.d1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '972.429', 'aut_weyl_index': 4, 'centralizer': '324.a1.a1', 'complements': ['162.a1.a1', '162.b1.a1', '162.d1.a1', '162.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.b1', '2.d1.c1'], 'contains': ['8.a1.a1', '12.d1.b1', '12.j1.b1'], 'core': '4.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5684, 1977, 8662, 2746, 2246, 2319, 5851, 7505], 'generators': [6, 36, 4, 48, 216], 'label': '648.297.4.d1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.b1', 'normal_contained_in': ['2.c1.a1', '2.d1.b1', '2.d1.c1'], 'normal_contains': ['8.a1.a1', '12.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.b1', 'projective_image': '648.297', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.d1.b1', 'subgroup_fusion': None, 'weyl_group': '324.37'}
  • id: 110362713
    {'ambient': '648.297', 'aut_centralizer_order': 36, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '54.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.b1', '36.k1.b1', '54.c1.a1', '54.n1.c1', '54.n1.d1'], 'contains': ['216.d1.a1', '324.b1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [511, -1, 2590, -1, 6962, -1, 1817, -1], 'generators': [109, 4], 'label': '648.297.108.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '108.h1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.h1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362714
    {'ambient': '648.297', 'aut_centralizer_order': 36, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '54.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1.a1', '36.m1.a1', '36.n1.a1', '54.d1.a1', '54.m1.a1', '54.m1.c1'], 'contains': ['216.a1.a1', '324.c1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [5450, -1, 3005, -1, 6000, -1, 3702, -1], 'generators': [327, 216], 'label': '648.297.108.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '108.i1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110362715
    {'ambient': '648.297', 'aut_centralizer_order': 36, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '54.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1.b1', '36.m1.b1', '36.n1.b1', '54.d1.a1', '54.m1.b1', '54.m1.d1'], 'contains': ['216.a1.a1', '324.c1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [5450, -1, 2880, -1, 6000, -1, 3804, -1], 'generators': [3, 216], 'label': '648.297.108.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '108.i1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.i1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110362716
    {'ambient': '648.297', 'aut_centralizer_order': 36, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '54.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1.a1', '36.o1.a1', '36.p1.a1', '36.q1.a1', '54.e1.a1', '54.l1.a1', '54.l1.c1'], 'contains': ['216.b1.a1', '324.c1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8221, -1, 6650, -1, 3953, -1, 6999, -1], 'generators': [327, 36], 'label': '648.297.108.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '108.j1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362717
    {'ambient': '648.297', 'aut_centralizer_order': 36, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '54.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1.b1', '36.o1.b1', '36.p1.b1', '36.q1.b1', '54.e1.a1', '54.l1.b1', '54.l1.d1'], 'contains': ['216.b1.a1', '324.c1.b1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8221, -1, 5407, -1, 3953, -1, 7101, -1], 'generators': [3, 36], 'label': '648.297.108.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '108.j1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.j1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362718
    {'ambient': '648.297', 'aut_centralizer_order': 36, 'aut_label': '108.k1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '54.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.m1.a1', '36.o1.a1', '54.f1.a1', '54.n1.a1', '54.n1.c1'], 'contains': ['216.d1.a1', '324.c1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1954, -1, 1240, -1, 7862, -1, 2294, -1], 'generators': [327, 4], 'label': '648.297.108.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '108.k1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362719
    {'ambient': '648.297', 'aut_centralizer_order': 36, 'aut_label': '108.k1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '54.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.m1.b1', '36.o1.b1', '54.f1.a1', '54.n1.b1', '54.n1.d1'], 'contains': ['216.d1.a1', '324.c1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1954, -1, 1079, -1, 7862, -1, 2395, -1], 'generators': [3, 4], 'label': '648.297.108.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '108.k1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.k1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362720
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '108.l1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.n1.a1', '36.o1.a1', '54.g1.a1'], 'contains': ['216.e1.a1', '324.c1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3504, -1, 687, -1, 8991, -1, 4743, -1], 'generators': [327, 40], 'label': '648.297.108.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1.a1', 'old_label': '108.l1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.l1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362721
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '108.l1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.n1.b1', '36.o1.b1', '54.g1.a1'], 'contains': ['216.e1.a1', '324.c1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3504, -1, 344, -1, 8991, -1, 5066, -1], 'generators': [3, 40], 'label': '648.297.108.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1.a1', 'old_label': '108.l1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.l1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362722
    {'ambient': '648.297', 'aut_centralizer_order': 36, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '54.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.r1.a1', '36.s1.a1', '36.t1.a1', '54.h1.a1', '54.n1.a1', '54.n1.d1'], 'contains': ['216.d1.a1', '324.d1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1150, -1, 1746, -1, 5839, -1, 1613, -1], 'generators': [114, 4], 'label': '648.297.108.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1.a1', 'old_label': '108.m1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110362723
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '216.102', 'aut_weyl_index': 18, 'centralizer': '108.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.a1'], 'contains': ['12.a1.a1', '12.c1.a1', '12.c1.b1', '18.a1.a1', '18.c1.a1', '18.d1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3917, 9030, 4215, 8273, 7153, 8985, 4148, 736], 'generators': [1, 216, 324, 36, 4], 'label': '648.297.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.a1', '12.c1.a1', '12.c1.b1', '18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 110362724
    {'ambient': '648.297', 'aut_centralizer_order': 36, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '54.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.r1.b1', '36.s1.b1', '36.t1.b1', '54.h1.a1', '54.n1.b1', '54.n1.c1'], 'contains': ['216.d1.a1', '324.d1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1150, -1, 3797, -1, 5839, -1, 1715, -1], 'generators': [6, 4], 'label': '648.297.108.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1.a1', 'old_label': '108.m1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.m1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110362725
    {'ambient': '648.297', 'aut_centralizer_order': 36, 'aut_label': '108.n1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '54.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.r1.a1', '36.u1.a1', '54.i1.a1', '54.m1.a1', '54.m1.d1'], 'contains': ['216.a1.a1', '324.d1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4035, -1, 4230, -1, 4656, -1, 2613, -1], 'generators': [114, 216], 'label': '648.297.108.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '108.n1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.n1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362726
    {'ambient': '648.297', 'aut_centralizer_order': 36, 'aut_label': '108.n1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '54.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.r1.b1', '36.u1.b1', '54.i1.a1', '54.m1.b1', '54.m1.c1'], 'contains': ['216.a1.a1', '324.d1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4035, -1, 5794, -1, 4656, -1, 2715, -1], 'generators': [6, 216], 'label': '648.297.108.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '108.n1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.n1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362727
    {'ambient': '648.297', 'aut_centralizer_order': 36, 'aut_label': '108.o1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '54.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.s1.a1', '36.u1.a1', '36.v1.a1', '54.j1.a1', '54.l1.a1', '54.l1.d1'], 'contains': ['216.b1.a1', '324.d1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7078, -1, 6812, -1, 2883, -1, 5955, -1], 'generators': [114, 36], 'label': '648.297.108.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '108.o1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.o1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362728
    {'ambient': '648.297', 'aut_centralizer_order': 36, 'aut_label': '108.o1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '54.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.s1.b1', '36.u1.b1', '36.v1.b1', '54.j1.a1', '54.l1.b1', '54.l1.c1'], 'contains': ['216.b1.a1', '324.d1.b1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7078, -1, 8216, -1, 2883, -1, 6088, -1], 'generators': [6, 36], 'label': '648.297.108.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '108.o1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.o1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362729
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '108.p1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.t1.a1', '36.u1.a1', '54.k1.a1'], 'contains': ['216.c1.a1', '324.d1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6005, -1, 5572, -1, 4336, -1, 1308, -1], 'generators': [114, 252], 'label': '648.297.108.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1.a1', 'old_label': '108.p1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.p1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362730
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '108.p1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.t1.b1', '36.u1.b1', '54.k1.a1'], 'contains': ['216.c1.a1', '324.d1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6005, -1, 7503, -1, 4336, -1, 1409, -1], 'generators': [6, 252], 'label': '648.297.108.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1.a1', 'old_label': '108.p1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.p1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362731
    {'ambient': '648.297', 'aut_centralizer_order': 216, 'aut_label': '162.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1.a1', '54.b1.a1', '54.c1.a1', '81.a1.a1'], 'contains': ['324.a1.a1', '324.b1.a1', '324.b1.b1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3988, -1, 4028, -1, 5354, -1, 3158, -1], 'generators': [1, 324], 'label': '648.297.162.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '162.a1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110362732
    {'ambient': '648.297', 'aut_centralizer_order': 72, 'aut_label': '162.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '27.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.d1.a1', '54.e1.a1', '54.f1.a1', '54.g1.a1', '81.a1.a1'], 'contains': ['324.a1.a1', '324.c1.a1', '324.c1.b1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4964, -1, 2932, -1, 6171, -1, 3913, -1], 'generators': [3, 324], 'label': '648.297.162.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '162.b1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110362733
    {'ambient': '648.297', 'aut_centralizer_order': 72, 'aut_label': '162.c1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '27.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.h1.a1', '54.i1.a1', '54.j1.a1', '54.k1.a1', '81.a1.a1'], 'contains': ['324.a1.a1', '324.d1.a1', '324.d1.b1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [5213, -1, 3599, -1, 4828, -1, 2504, -1], 'generators': [6, 324], 'label': '648.297.162.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1.a1', 'old_label': '162.c1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110362734
    {'ambient': '648.297', 'aut_centralizer_order': 2, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1944.2684', 'aut_weyl_index': 2, 'centralizer': '324.a1.a1', 'complements': ['108.h1.a1', '108.h1.b1', '108.k1.b1', '108.k1.a1', '108.l1.b1', '108.l1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.d1.a1', '12.d1.b1', '18.n1.a1', '18.o1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8115, 970, 8167, 2272, 952, 787, 6668, 9458], 'generators': [6, 36, 324, 48, 216], 'label': '648.297.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['12.b1.a1', '12.d1.a1', '12.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '324.37', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '324.37'}
  • id: 110362735
    {'ambient': '648.297', 'aut_centralizer_order': 12, 'aut_label': '162.d1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3888, 'centralizer': '81.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.l1.a1', '54.m1.a1', '54.n1.a1', '81.a1.a1'], 'contains': ['324.b1.a1', '324.c1.a1', '324.d1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [4634, -1, 3407, -1, 5011, -1, 3376, -1], 'generators': [433, 114], 'label': '648.297.162.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '162.d1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110362736
    {'ambient': '648.297', 'aut_centralizer_order': 12, 'aut_label': '162.d1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3888, 'centralizer': '81.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.l1.b1', '54.m1.b1', '54.n1.b1', '81.a1.a1'], 'contains': ['324.b1.a1', '324.c1.b1', '324.d1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [4634, -1, 4757, -1, 5011, -1, 3492, -1], 'generators': [1, 6], 'label': '648.297.162.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '162.d1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110362737
    {'ambient': '648.297', 'aut_centralizer_order': 12, 'aut_label': '162.d1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3888, 'centralizer': '81.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.l1.c1', '54.m1.c1', '54.n1.c1', '81.a1.a1'], 'contains': ['324.b1.b1', '324.c1.a1', '324.d1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [4634, -1, 3836, -1, 5011, -1, 2940, -1], 'generators': [325, 6], 'label': '648.297.162.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '162.d1.c1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.d1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110362738
    {'ambient': '648.297', 'aut_centralizer_order': 12, 'aut_label': '162.d1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3888, 'centralizer': '81.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.l1.d1', '54.m1.d1', '54.n1.d1', '81.a1.a1'], 'contains': ['324.b1.b1', '324.c1.b1', '324.d1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [4634, -1, 3123, -1, 5011, -1, 2824, -1], 'generators': [109, 114], 'label': '648.297.162.d1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '162.d1.d1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.d1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110362739
    {'ambient': '648.297', 'aut_centralizer_order': 1944, 'aut_label': '216.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.b1.a1', '72.c1.a1', '108.a1.a1', '108.g1.a1', '108.g1.b1', '108.i1.a1', '108.i1.b1', '108.n1.a1', '108.n1.b1'], 'contains': ['648.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4316, 5895, 4337, 5662, 5358, 6017, 3269, 3803], 'generators': [216], 'label': '648.297.216.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '216.a1.a1', 'normal_contained_in': ['72.a1.a1', '72.b1.a1', '108.a1.a1'], 'normal_contains': ['648.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.a1.a1', 'projective_image': '648.297', 'quotient_action_image': '2.1', 'quotient_action_kernel': '108.27', 'quotient_action_kernel_order': 108, 'quotient_fusion': None, 'short_label': '216.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110362740
    {'ambient': '648.297', 'aut_centralizer_order': 1944, 'aut_label': '216.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.d1.a1', '72.e1.a1', '72.f1.a1', '108.b1.a1', '108.f1.a1', '108.f1.b1', '108.j1.a1', '108.j1.b1', '108.o1.a1', '108.o1.b1'], 'contains': ['648.a1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7587, 4055, 7523, 4338, 3549, 4495, 6466, 4853], 'generators': [36], 'label': '648.297.216.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '216.b1.a1', 'normal_contained_in': ['72.a1.a1', '108.b1.a1'], 'normal_contains': ['648.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.b1.a1', 'projective_image': '648.297', 'quotient_action_image': '2.1', 'quotient_action_kernel': '108.25', 'quotient_action_kernel_order': 108, 'quotient_fusion': None, 'short_label': '216.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110362741
    {'ambient': '648.297', 'aut_centralizer_order': 972, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.g1.a1', '108.c1.a1', '108.p1.a1', '108.p1.b1'], 'contains': ['648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5851, -1, 5613, -1, 4496, -1, 1460, -1], 'generators': [252], 'label': '648.297.216.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '216.c1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110362742
    {'ambient': '648.297', 'aut_centralizer_order': 648, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '6.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '72.d1.a1', '72.g1.a1', '108.d1.a1', '108.h1.a1', '108.h1.b1', '108.k1.a1', '108.k1.b1', '108.m1.a1', '108.m1.b1'], 'contains': ['648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1854, -1, 1833, -1, 7256, -1, 2028, -1], 'generators': [4], 'label': '648.297.216.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '216.d1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110362743
    {'ambient': '648.297', 'aut_centralizer_order': 324, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.a1', '72.d1.a1', '72.g1.a1', '108.e1.a1', '108.l1.a1', '108.l1.b1'], 'contains': ['648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3483, -1, 819, -1, 7782, -1, 4446, -1], 'generators': [40], 'label': '648.297.216.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '216.e1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110362744
    {'ambient': '648.297', 'aut_centralizer_order': 3888, 'aut_label': '324.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3888, 'centralizer': '1.a1.a1', 'complements': ['2.d1.b1', '2.d1.c1', '2.d1.a1', '2.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '108.b1.a1', '108.c1.a1', '108.d1.a1', '108.e1.a1', '162.a1.a1', '162.b1.a1', '162.c1.a1'], 'contains': ['648.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4513, 4913, 3717, 4955, 5518, 5256, 3168, 4328], 'generators': [324], 'label': '648.297.324.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '324.a1.a1', 'normal_contained_in': ['108.b1.a1', '108.a1.a1'], 'normal_contains': ['648.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '324.a1.a1', 'projective_image': '324.37', 'quotient_action_image': '1.1', 'quotient_action_kernel': '324.37', 'quotient_action_kernel_order': 324, 'quotient_fusion': None, 'short_label': '324.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110362745
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '648.603', 'aut_weyl_index': 6, 'centralizer': '108.b1.a1', 'complements': ['324.d1.b1', '324.d1.a1', '324.c1.b1', '324.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '6.a1.a1', '6.c1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6615, 8234, 8510, 9194, 2870, 7634, 6277, 1669], 'generators': [1, 216, 4, 324, 84, 36], 'label': '648.297.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '324.37', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 110362746
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.48', 'aut_weyl_index': 54, 'centralizer': '36.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.f1.a1', '12.f1.b1', '18.b1.a1', '18.c1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7771, -1, 9072, -1, 1623, -1, 7783, -1], 'generators': [1, 216, 324, 84, 36], 'label': '648.297.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110362747
    {'ambient': '648.297', 'aut_centralizer_order': 216, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3888, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.f1.a1', '108.g1.a1', '108.h1.a1', '162.a1.a1', '162.d1.a1', '162.d1.b1'], 'contains': ['648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4052, -1, 4270, -1, 5187, -1, 3376, -1], 'generators': [1], 'label': '648.297.324.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '324.b1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110362748
    {'ambient': '648.297', 'aut_centralizer_order': 216, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3888, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.f1.b1', '108.g1.b1', '108.h1.b1', '162.a1.a1', '162.d1.c1', '162.d1.d1'], 'contains': ['648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4052, -1, 3902, -1, 5187, -1, 3049, -1], 'generators': [109], 'label': '648.297.324.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '324.b1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110362749
    {'ambient': '648.297', 'aut_centralizer_order': 72, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3888, 'centralizer': '27.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.i1.a1', '108.j1.a1', '108.k1.a1', '108.l1.a1', '162.b1.a1', '162.d1.a1', '162.d1.c1'], 'contains': ['648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4667, -1, 3182, -1, 6000, -1, 3534, -1], 'generators': [327], 'label': '648.297.324.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '324.c1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110362750
    {'ambient': '648.297', 'aut_centralizer_order': 72, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3888, 'centralizer': '27.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.i1.b1', '108.j1.b1', '108.k1.b1', '108.l1.b1', '162.b1.a1', '162.d1.b1', '162.d1.d1'], 'contains': ['648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4667, -1, 3005, -1, 6000, -1, 3692, -1], 'generators': [3], 'label': '648.297.324.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '324.c1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110362751
    {'ambient': '648.297', 'aut_centralizer_order': 72, 'aut_label': '324.d1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3888, 'centralizer': '27.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.m1.a1', '108.n1.a1', '108.o1.a1', '108.p1.a1', '162.c1.a1', '162.d1.a1', '162.d1.d1'], 'contains': ['648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4905, -1, 3441, -1, 4828, -1, 2719, -1], 'generators': [114], 'label': '648.297.324.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1.a1', 'old_label': '324.d1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110362752
    {'ambient': '648.297', 'aut_centralizer_order': 72, 'aut_label': '324.d1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3888, 'centralizer': '27.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.m1.b1', '108.n1.b1', '108.o1.b1', '108.p1.b1', '162.c1.a1', '162.d1.b1', '162.d1.c1'], 'contains': ['648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4905, -1, 4181, -1, 4828, -1, 2933, -1], 'generators': [6], 'label': '648.297.324.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1.a1', 'old_label': '324.d1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110362753
    {'ambient': '648.297', 'aut_centralizer_order': None, 'aut_label': '648.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '216.b1.a1', '216.c1.a1', '216.d1.a1', '216.e1.a1', '324.a1.a1', '324.b1.a1', '324.b1.b1', '324.c1.a1', '324.c1.b1', '324.d1.a1', '324.d1.b1'], 'contains': [], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4513, 4913, 3810, 4955, 5358, 5256, 3219, 4328], 'generators': [], 'label': '648.297.648.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '648.a1.a1', 'normal_contained_in': ['216.b1.a1', '216.a1.a1', '324.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '648.a1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110362754
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 54, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.b1.a1'], 'contains': ['12.a1.a1', '12.g1.a1', '12.g1.b1', '18.e1.a1', '18.f1.a1', '18.g1.a1', '18.h1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5109, -1, 2370, -1, 8463, -1, 5019, -1], 'generators': [3, 36, 324, 216, 4], 'label': '648.297.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.d1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362755
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '216.111', 'aut_weyl_index': 18, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.h1.a1', '12.h1.b1', '18.e1.a1', '18.i1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8717, -1, 7454, -1, 1957, -1, 8380, -1], 'generators': [3, 36, 324, 216, 480], 'label': '648.297.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '36.4'}
  • id: 110362756
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '108.26', 'aut_weyl_index': 36, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['12.e1.a1', '12.i1.a1', '12.i1.b1', '18.e1.a1', '18.j1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8431, -1, 7101, -1, 3621, -1, 9490, -1], 'generators': [3, 36, 324, 216, 52], 'label': '648.297.6.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '6.f1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.a1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 110362757
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 54, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.b1.a1'], 'contains': ['12.a1.a1', '12.j1.a1', '12.j1.b1', '18.k1.a1', '18.l1.a1', '18.m1.a1', '18.n1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4264, -1, 2840, -1, 5699, -1, 3228, -1], 'generators': [6, 216, 324, 4, 36], 'label': '648.297.6.g1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.g1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362758
    {'ambient': '648.297', 'aut_centralizer_order': 1, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '324.118', 'aut_weyl_index': 12, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.d1.a1', '12.f1.a1', '12.h1.a1', '18.p1.a1', '18.q1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7099, -1, 7892, -1, 1291, -1, 7994, -1], 'generators': [1, 36, 114, 48, 216], 'label': '648.297.6.h1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.h1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1.a1', 'subgroup_fusion': None, 'weyl_group': '108.16'}
  • id: 110362759
    {'ambient': '648.297', 'aut_centralizer_order': 1, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '324.118', 'aut_weyl_index': 12, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.b1', '3.a1.a1'], 'contains': ['12.d1.b1', '12.f1.a1', '12.h1.b1', '18.p1.b1', '18.q1.b1'], 'core': '12.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7099, -1, 9474, -1, 1291, -1, 8186, -1], 'generators': [1, 36, 6, 48, 216], 'label': '648.297.6.h1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.h1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1.b1', 'subgroup_fusion': None, 'weyl_group': '108.16'}
  • id: 110362760
    {'ambient': '648.297', 'aut_centralizer_order': 1, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '324.118', 'aut_weyl_index': 12, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.c1', '3.a1.a1'], 'contains': ['12.d1.b1', '12.f1.b1', '12.h1.a1', '18.p1.c1', '18.q1.c1'], 'core': '12.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7099, -1, 8810, -1, 1291, -1, 7572, -1], 'generators': [109, 36, 6, 48, 216], 'label': '648.297.6.h1.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.h1.c1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1.c1', 'subgroup_fusion': None, 'weyl_group': '108.16'}
  • id: 110362761
    {'ambient': '648.297', 'aut_centralizer_order': 1, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '324.118', 'aut_weyl_index': 12, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.d1', '3.a1.a1'], 'contains': ['12.d1.a1', '12.f1.b1', '12.h1.b1', '18.p1.d1', '18.q1.d1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7099, -1, 7726, -1, 1291, -1, 7380, -1], 'generators': [109, 36, 114, 48, 216], 'label': '648.297.6.h1.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.h1.d1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1.d1', 'subgroup_fusion': None, 'weyl_group': '108.16'}
  • id: 110362762
    {'ambient': '648.297', 'aut_centralizer_order': 3, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '108.40', 'aut_weyl_index': 36, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.b1.a1'], 'contains': ['12.c1.a1', '12.g1.a1', '12.j1.a1', '18.q1.a1', '18.r1.a1', '18.s1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3327, -1, 3395, -1, 6124, -1, 4360, -1], 'generators': [1, 216, 114, 4, 36], 'label': '648.297.6.i1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.i1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1.a1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 110362763
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '648.604', 'aut_weyl_index': 6, 'centralizer': '108.a1.a1', 'complements': ['324.d1.b1', '324.d1.a1', '324.b1.a1', '324.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.c1.b1', '6.d1.a1', '6.e1.a1', '6.f1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7082, 3918, 7216, 2817, 3369, 3967, 6940, 5086], 'generators': [3, 216, 36, 324, 4, 480], 'label': '648.297.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.c1.a1', '4.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '324.37', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '108.16'}
  • id: 110362764
    {'ambient': '648.297', 'aut_centralizer_order': 3, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '108.40', 'aut_weyl_index': 36, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.b1', '3.b1.a1'], 'contains': ['12.c1.a1', '12.g1.b1', '12.j1.b1', '18.q1.b1', '18.r1.b1', '18.s1.b1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3327, -1, 4674, -1, 6124, -1, 4550, -1], 'generators': [1, 216, 6, 4, 36], 'label': '648.297.6.i1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.i1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1.b1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 110362765
    {'ambient': '648.297', 'aut_centralizer_order': 3, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '108.40', 'aut_weyl_index': 36, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.c1', '3.b1.a1'], 'contains': ['12.c1.b1', '12.g1.a1', '12.j1.b1', '18.q1.c1', '18.r1.c1', '18.s1.c1'], 'core': '12.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [3327, -1, 3883, -1, 6124, -1, 3715, -1], 'generators': [109, 216, 6, 4, 36], 'label': '648.297.6.i1.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.i1.c1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1.c1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 110362766
    {'ambient': '648.297', 'aut_centralizer_order': 3, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '108.40', 'aut_weyl_index': 36, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.d1', '3.b1.a1'], 'contains': ['12.c1.b1', '12.g1.b1', '12.j1.a1', '18.q1.d1', '18.r1.d1', '18.s1.d1'], 'core': '12.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [3327, -1, 2658, -1, 6124, -1, 3525, -1], 'generators': [109, 216, 114, 4, 36], 'label': '648.297.6.i1.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.i1.d1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1.d1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 110362767
    {'ambient': '648.297', 'aut_centralizer_order': 36, 'aut_label': '8.a1', 'aut_quo_index': 42, 'aut_stab_index': 1, 'aut_weyl_group': '108.38', 'aut_weyl_index': 36, 'centralizer': '36.a1.a1', 'complements': ['81.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.c1.a1', '4.c1.b1', '4.d1.a1', '4.d1.b1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.c1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6276, 4428, 8659, 5429, 2240, 4326, 6941, 5122], 'generators': [4, 84], 'label': '648.297.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.c1.a1', '4.c1.b1', '4.d1.a1', '4.d1.b1'], 'normal_contains': ['24.a1.a1', '24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '648.297', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362768
    {'ambient': '648.297', 'aut_centralizer_order': 2, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '216.111', 'aut_weyl_index': 18, 'centralizer': '162.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['18.b1.a1', '18.i1.a1', '18.o1.a1', '18.p1.a1', '18.p1.b1', '18.p1.c1', '18.p1.d1', '27.a1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9058, -1, 8355, -1, 571, -1, 8598, -1], 'generators': [1, 36, 6, 324, 48], 'label': '648.297.9.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 110362769
    {'ambient': '648.297', 'aut_centralizer_order': 3, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.192', 'aut_weyl_index': 27, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.b1.a1'], 'contains': ['18.c1.a1', '18.e1.a1', '18.n1.a1', '18.q1.a1', '18.q1.b1', '18.q1.c1', '18.q1.d1', '27.a1.a1', '27.b1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6073, -1, 6579, -1, 4122, -1, 5479, -1], 'generators': [1, 216, 6, 324, 36], 'label': '648.297.9.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '9.b1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362770
    {'ambient': '648.297', 'aut_centralizer_order': 3, 'aut_label': '9.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.192', 'aut_weyl_index': 27, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['18.d1.a1', '18.h1.a1', '18.l1.a1', '18.r1.a1', '18.r1.b1', '18.r1.c1', '18.r1.d1', '27.a1.a1', '27.c1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [906, -1, 2421, -1, 6795, -1, 3920, -1], 'generators': [1, 36, 6, 324, 4], 'label': '648.297.9.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '9.c1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.c1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362771
    {'ambient': '648.297', 'aut_centralizer_order': 3, 'aut_label': '9.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.192', 'aut_weyl_index': 27, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['18.a1.a1', '18.f1.a1', '18.k1.a1', '18.s1.a1', '18.s1.b1', '18.s1.c1', '18.s1.d1', '27.b1.a1', '27.c1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2845, -1, 3898, -1, 6447, -1, 1991, -1], 'generators': [1, 216, 6, 324, 4], 'label': '648.297.9.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '9.d1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.d1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362772
    {'ambient': '648.297', 'aut_centralizer_order': 324, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.d1.a1', '6.g1.a1'], 'contains': ['24.a1.a1', '36.a1.a1', '36.b1.a1', '36.d1.a1', '36.e1.a1', '36.h1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4449, 5747, 2631, 5465, 8283, 5753, 4091, 4139], 'generators': [324, 4, 36, 216], 'label': '648.297.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '36.a1.a1', '36.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '324.37', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110362773
    {'ambient': '648.297', 'aut_centralizer_order': 108, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '36.12', 'aut_weyl_index': 108, 'centralizer': '12.b1.a1', 'complements': ['54.n1.b1', '54.n1.c1', '54.n1.a1', '54.n1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.a1', '6.c1.a1', '6.e1.a1'], 'contains': ['24.b1.a1', '36.a1.a1', '36.f1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8427, 2724, 8764, 2039, 1627, 2868, 7589, 6128], 'generators': [324, 84, 216, 36], 'label': '648.297.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.a1.a1', '6.b1.a1'], 'normal_contains': ['24.b1.a1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '324.37', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110362774
    {'ambient': '648.297', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1944.2684', 'aut_weyl_index': 2, 'centralizer': '324.a1.a1', 'complements': ['324.b1.a1', '324.b1.b1', '324.c1.b1', '324.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.d1.a1', '4.d1.b1', '6.b1.a1', '6.g1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6202, 1119, 8113, 806, 2157, 1590, 5651, 8503], 'generators': [6, 36, 216, 324, 4, 48], 'label': '648.297.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.d1.a1', '4.d1.b1', '6.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '324.37', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '324.37'}
  • id: 110362775
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '12.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '108.17', 'aut_weyl_index': 36, 'centralizer': '108.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1', '6.i1.a1', '6.i1.b1'], 'contains': ['24.a1.a1', '36.c1.a1', '36.j1.a1', '36.k1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3524, 7761, 4894, 7254, 6904, 7464, 4550, 1749], 'generators': [1, 36, 4, 216], 'label': '648.297.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '36.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 110362776
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '12.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '108.17', 'aut_weyl_index': 36, 'centralizer': '108.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.a1.a1', '6.i1.c1', '6.i1.d1'], 'contains': ['24.a1.a1', '36.c1.b1', '36.j1.b1', '36.k1.b1'], 'core': '12.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3524, 7761, 3461, 9186, 6904, 7464, 3671, 2958], 'generators': [109, 36, 4, 216], 'label': '648.297.12.c1.b1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.c1.b1', 'normal_contained_in': ['4.b1.b1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '36.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.b1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 110362777
    {'ambient': '648.297', 'aut_centralizer_order': 2, 'aut_label': '12.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '972.429', 'aut_weyl_index': 4, 'centralizer': '324.a1.a1', 'complements': ['54.c1.a1', '54.f1.a1', '54.g1.a1', '54.n1.b1', '54.n1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.b1.a1', '6.h1.a1', '6.h1.d1'], 'contains': ['24.b1.a1', '36.u1.a1', '36.v1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7375, 1132, 7903, 3184, 1041, 1516, 7087, 8401], 'generators': [114, 48, 216, 36], 'label': '648.297.12.d1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.d1.a1', 'normal_contained_in': ['4.d1.a1', '6.b1.a1'], 'normal_contains': ['24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '648.297', 'quotient_action_image': '6.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '324.37'}
  • id: 110362778
    {'ambient': '648.297', 'aut_centralizer_order': 2, 'aut_label': '12.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '972.429', 'aut_weyl_index': 4, 'centralizer': '324.a1.a1', 'complements': ['54.c1.a1', '54.f1.a1', '54.g1.a1', '54.n1.a1', '54.n1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1', '6.b1.a1', '6.h1.b1', '6.h1.c1'], 'contains': ['24.b1.a1', '36.u1.b1', '36.v1.b1'], 'core': '12.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7375, 1132, 9465, 4006, 1041, 1516, 7217, 7505], 'generators': [6, 48, 216, 36], 'label': '648.297.12.d1.b1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.d1.b1', 'normal_contained_in': ['4.d1.b1', '6.b1.a1'], 'normal_contains': ['24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.b1', 'projective_image': '648.297', 'quotient_action_image': '6.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.d1.b1', 'subgroup_fusion': None, 'weyl_group': '324.37'}
  • id: 110362779
    {'ambient': '648.297', 'aut_centralizer_order': 108, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '18.3', 'aut_weyl_index': 216, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.f1.a1'], 'contains': ['24.c1.a1', '36.a1.a1', '36.g1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8006, -1, 8150, -1, 2547, -1, 9384, -1], 'generators': [324, 88, 216, 36], 'label': '648.297.12.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.e1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362780
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.12', 'aut_weyl_index': 108, 'centralizer': '36.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.c1.a1', '6.h1.a1', '6.h1.b1'], 'contains': ['24.b1.a1', '36.i1.a1', '36.j1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7059, -1, 9603, -1, 1295, -1, 7800, -1], 'generators': [1, 84, 36, 216], 'label': '648.297.12.f1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110362781
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.12', 'aut_weyl_index': 108, 'centralizer': '36.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.c1.a1', '6.h1.c1', '6.h1.d1'], 'contains': ['24.b1.a1', '36.i1.b1', '36.j1.b1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7059, -1, 9037, -1, 1295, -1, 7378, -1], 'generators': [109, 84, 36, 216], 'label': '648.297.12.f1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.f1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110362782
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 108, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.d1.a1', '6.i1.a1', '6.i1.c1'], 'contains': ['24.a1.a1', '36.l1.a1', '36.m1.a1', '36.n1.a1', '36.o1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5242, -1, 3029, -1, 8644, -1, 4784, -1], 'generators': [327, 216, 4, 36], 'label': '648.297.12.g1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.g1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362783
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 108, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '6.d1.a1', '6.i1.b1', '6.i1.d1'], 'contains': ['24.a1.a1', '36.l1.b1', '36.m1.b1', '36.n1.b1', '36.o1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5242, -1, 1837, -1, 8644, -1, 5019, -1], 'generators': [3, 216, 4, 36], 'label': '648.297.12.g1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.g1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362784
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '108.26', 'aut_weyl_index': 36, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.e1.a1', '6.h1.a1', '6.h1.c1'], 'contains': ['24.b1.a1', '36.l1.a1', '36.p1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6694, -1, 7626, -1, 1961, -1, 7992, -1], 'generators': [327, 216, 480, 36], 'label': '648.297.12.h1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.h1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': '36.4'}
  • id: 110362785
    {'ambient': '648.297', 'aut_centralizer_order': 1, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '972.429', 'aut_weyl_index': 4, 'centralizer': '324.a1.a1', 'complements': ['324.a1.a1', '324.d1.b1', '324.b1.b1', '324.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.d1.a1', '6.h1.a1', '6.i1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5826, 6244, 7724, 5581, 2514, 5943, 6503, 2834], 'generators': [1, 216, 36, 114, 4, 48], 'label': '648.297.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.a1', '4.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '648.297', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': '324.37'}
  • id: 110362786
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '108.26', 'aut_weyl_index': 36, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '6.e1.a1', '6.h1.b1', '6.h1.d1'], 'contains': ['24.b1.a1', '36.l1.b1', '36.p1.b1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6694, -1, 7412, -1, 1961, -1, 8186, -1], 'generators': [3, 216, 480, 36], 'label': '648.297.12.h1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.h1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.b1', 'subgroup_fusion': None, 'weyl_group': '36.4'}
  • id: 110362787
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '54.6', 'aut_weyl_index': 72, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.f1.a1'], 'contains': ['24.c1.a1', '36.l1.a1', '36.q1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7694, -1, 7246, -1, 2881, -1, 9596, -1], 'generators': [327, 216, 52, 36], 'label': '648.297.12.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '12.i1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.a1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 110362788
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '54.6', 'aut_weyl_index': 72, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '6.f1.a1'], 'contains': ['24.c1.a1', '36.l1.b1', '36.q1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7694, -1, 6987, -1, 2881, -1, 9790, -1], 'generators': [3, 216, 52, 36], 'label': '648.297.12.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '12.i1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.b1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 110362789
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 108, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.g1.a1', '6.i1.a1', '6.i1.d1'], 'contains': ['24.a1.a1', '36.r1.a1', '36.s1.a1', '36.t1.a1', '36.u1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3961, -1, 2828, -1, 5269, -1, 2780, -1], 'generators': [114, 4, 36, 216], 'label': '648.297.12.j1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.j1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362790
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 108, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1', '6.g1.a1', '6.i1.b1', '6.i1.c1'], 'contains': ['24.a1.a1', '36.r1.b1', '36.s1.b1', '36.t1.b1', '36.u1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3961, -1, 4352, -1, 5269, -1, 3015, -1], 'generators': [6, 4, 36, 216], 'label': '648.297.12.j1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.j1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362791
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '18.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '216.102', 'aut_weyl_index': 18, 'centralizer': '108.b1.a1', 'complements': ['36.v1.b1', '36.v1.a1', '36.p1.b1', '36.p1.a1', '36.q1.b1', '36.q1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '9.d1.a1'], 'contains': ['36.b1.a1', '36.c1.a1', '36.c1.b1', '54.b1.a1', '54.c1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2320, 9030, 3977, 8273, 7621, 9218, 1903, 539], 'generators': [1, 324, 4, 216], 'label': '648.297.18.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['36.b1.a1', '36.c1.a1', '36.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '324.37', 'quotient_action_image': '6.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 110362792
    {'ambient': '648.297', 'aut_centralizer_order': 36, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.5', 'aut_weyl_index': 324, 'centralizer': '18.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '9.a1.a1'], 'contains': ['36.f1.a1', '36.i1.a1', '36.i1.b1', '54.a1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9311, -1, 9292, -1, 558, -1, 8776, -1], 'generators': [1, 324, 84, 36], 'label': '648.297.18.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110362793
    {'ambient': '648.297', 'aut_centralizer_order': 54, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 162, 'centralizer': '36.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.c1.a1', '9.b1.a1'], 'contains': ['36.a1.a1', '36.j1.a1', '36.j1.b1', '54.a1.a1', '54.b1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5869, -1, 6922, -1, 4284, -1, 6124, -1], 'generators': [1, 324, 36, 216], 'label': '648.297.18.c1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.c1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110362794
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 162, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '9.c1.a1'], 'contains': ['36.e1.a1', '36.k1.a1', '36.k1.b1', '54.a1.a1', '54.c1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [868, -1, 2827, -1, 7957, -1, 3885, -1], 'generators': [1, 324, 36, 4], 'label': '648.297.18.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.d1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110362795
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 162, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.e1.a1', '6.f1.a1', '9.b1.a1'], 'contains': ['36.a1.a1', '36.l1.a1', '36.l1.b1', '54.d1.a1', '54.e1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8433, -1, 5494, -1, 4585, -1, 6766, -1], 'generators': [3, 324, 216, 36], 'label': '648.297.18.e1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.e1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110362796
    {'ambient': '648.297', 'aut_centralizer_order': 1, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '972.429', 'aut_weyl_index': 4, 'centralizer': '324.a1.a1', 'complements': ['324.a1.a1', '324.d1.a1', '324.b1.b1', '324.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.b1', '4.d1.b1', '6.h1.b1', '6.i1.b1'], 'core': '2.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5826, 6244, 8782, 6672, 2514, 5943, 6675, 6448], 'generators': [1, 216, 36, 6, 4, 48], 'label': '648.297.2.d1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.b1', '4.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.b1', 'projective_image': '648.297', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.d1.b1', 'subgroup_fusion': None, 'weyl_group': '324.37'}
  • id: 110362797
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 162, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '9.d1.a1'], 'contains': ['36.b1.a1', '36.m1.a1', '36.m1.b1', '54.d1.a1', '54.f1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4195, -1, 1656, -1, 8980, -1, 2346, -1], 'generators': [3, 324, 216, 4], 'label': '648.297.18.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '18.f1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110362798
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1'], 'contains': ['36.d1.a1', '36.n1.a1', '36.n1.b1', '54.d1.a1', '54.g1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5030, -1, 755, -1, 9653, -1, 5468, -1], 'generators': [3, 324, 216, 40], 'label': '648.297.18.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1.a1', 'old_label': '18.g1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362799
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 54, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '9.c1.a1'], 'contains': ['36.e1.a1', '36.o1.a1', '36.o1.b1', '54.e1.a1', '54.f1.a1', '54.g1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1975, -1, 329, -1, 9316, -1, 5254, -1], 'generators': [3, 324, 4, 36], 'label': '648.297.18.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.h1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362800
    {'ambient': '648.297', 'aut_centralizer_order': 12, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '108.26', 'aut_weyl_index': 36, 'centralizer': '54.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '9.a1.a1'], 'contains': ['36.f1.a1', '36.p1.a1', '36.p1.b1', '54.e1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9944, -1, 8273, -1, 839, -1, 9206, -1], 'generators': [3, 324, 480, 36], 'label': '648.297.18.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.i1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.i1.a1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 110362801
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '18.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '108.26', 'aut_weyl_index': 36, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1'], 'contains': ['36.g1.a1', '36.q1.a1', '36.q1.b1', '54.e1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9573, -1, 7674, -1, 3133, -1, 9950, -1], 'generators': [3, 324, 52, 36], 'label': '648.297.18.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '18.j1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.j1.a1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 110362802
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '18.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 162, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '9.d1.a1'], 'contains': ['36.b1.a1', '36.r1.a1', '36.r1.b1', '54.h1.a1', '54.i1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2793, -1, 3468, -1, 5906, -1, 1240, -1], 'generators': [6, 324, 4, 216], 'label': '648.297.18.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '18.k1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.k1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110362803
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '18.l1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 162, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '9.c1.a1'], 'contains': ['36.e1.a1', '36.s1.a1', '36.s1.b1', '54.h1.a1', '54.j1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1231, -1, 1328, -1, 6207, -1, 3228, -1], 'generators': [6, 324, 4, 36], 'label': '648.297.18.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.l1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.l1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110362804
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '18.m1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1'], 'contains': ['36.h1.a1', '36.t1.a1', '36.t1.b1', '54.h1.a1', '54.k1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4476, -1, 1867, -1, 5605, -1, 494, -1], 'generators': [6, 324, 4, 252], 'label': '648.297.18.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1.a1', 'old_label': '18.m1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.m1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362805
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '18.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 54, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.g1.a1', '9.b1.a1'], 'contains': ['36.a1.a1', '36.u1.a1', '36.u1.b1', '54.i1.a1', '54.j1.a1', '54.k1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6353, -1, 6477, -1, 3418, -1, 5681, -1], 'generators': [6, 324, 36, 216], 'label': '648.297.18.n1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.n1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.n1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362806
    {'ambient': '648.297', 'aut_centralizer_order': 4, 'aut_label': '18.o1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '108.26', 'aut_weyl_index': 36, 'centralizer': '162.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '9.a1.a1'], 'contains': ['36.f1.a1', '36.v1.a1', '36.v1.b1', '54.j1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9758, -1, 8985, -1, 79, -1, 8346, -1], 'generators': [6, 324, 48, 36], 'label': '648.297.18.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.o1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.o1.a1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 110362807
    {'ambient': '648.297', 'aut_centralizer_order': 1, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '972.429', 'aut_weyl_index': 4, 'centralizer': '324.a1.a1', 'complements': ['324.a1.a1', '324.d1.a1', '324.b1.a1', '324.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.b1', '4.c1.a1', '4.d1.b1', '6.h1.c1', '6.i1.c1'], 'core': '2.d1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [5826, 6244, 8313, 4490, 2514, 5943, 6050, 3723], 'generators': [109, 216, 36, 6, 4, 48], 'label': '648.297.2.d1.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.c1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.b1', '4.c1.a1', '4.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.c1', 'projective_image': '648.297', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.d1.c1', 'subgroup_fusion': None, 'weyl_group': '324.37'}
  • id: 110362809
    {'ambient': '648.297', 'aut_centralizer_order': 2, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '54.6', 'aut_weyl_index': 72, 'centralizer': '162.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.b1', '9.a1.a1'], 'contains': ['36.i1.a1', '36.p1.b1', '36.v1.b1', '54.l1.b1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8966, -1, 9953, -1, 277, -1, 9080, -1], 'generators': [1, 6, 48, 36], 'label': '648.297.18.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.p1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.p1.b1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 110362810
    {'ambient': '648.297', 'aut_centralizer_order': 2, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '54.6', 'aut_weyl_index': 72, 'centralizer': '162.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.c1', '9.a1.a1'], 'contains': ['36.i1.b1', '36.p1.a1', '36.v1.b1', '54.l1.c1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8966, -1, 9139, -1, 277, -1, 8598, -1], 'generators': [325, 6, 48, 36], 'label': '648.297.18.p1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.p1.c1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.p1.c1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 110362811
    {'ambient': '648.297', 'aut_centralizer_order': 2, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '54.6', 'aut_weyl_index': 72, 'centralizer': '162.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.d1', '9.a1.a1'], 'contains': ['36.i1.b1', '36.p1.b1', '36.v1.a1', '54.l1.d1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8966, -1, 8502, -1, 277, -1, 8472, -1], 'generators': [109, 114, 48, 36], 'label': '648.297.18.p1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.p1.d1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.p1.d1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 110362812
    {'ambient': '648.297', 'aut_centralizer_order': 3, 'aut_label': '18.q1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.10', 'aut_weyl_index': 108, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '6.i1.a1', '9.b1.a1'], 'contains': ['36.j1.a1', '36.l1.a1', '36.u1.a1', '54.l1.a1', '54.m1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6094, -1, 5910, -1, 3694, -1, 6277, -1], 'generators': [1, 114, 36, 216], 'label': '648.297.18.q1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.q1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.q1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362813
    {'ambient': '648.297', 'aut_centralizer_order': 3, 'aut_label': '18.q1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.10', 'aut_weyl_index': 108, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.b1', '6.i1.b1', '9.b1.a1'], 'contains': ['36.j1.a1', '36.l1.b1', '36.u1.b1', '54.l1.b1', '54.m1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6094, -1, 8077, -1, 3694, -1, 6613, -1], 'generators': [1, 6, 36, 216], 'label': '648.297.18.q1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.q1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.q1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362814
    {'ambient': '648.297', 'aut_centralizer_order': 3, 'aut_label': '18.q1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.10', 'aut_weyl_index': 108, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.c1', '6.i1.c1', '9.b1.a1'], 'contains': ['36.j1.b1', '36.l1.a1', '36.u1.b1', '54.l1.c1', '54.m1.c1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6094, -1, 6782, -1, 3694, -1, 5971, -1], 'generators': [109, 6, 36, 216], 'label': '648.297.18.q1.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.q1.c1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.q1.c1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362815
    {'ambient': '648.297', 'aut_centralizer_order': 3, 'aut_label': '18.q1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.10', 'aut_weyl_index': 108, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.d1', '6.i1.d1', '9.b1.a1'], 'contains': ['36.j1.b1', '36.l1.b1', '36.u1.a1', '54.l1.d1', '54.m1.d1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6094, -1, 5672, -1, 3694, -1, 5856, -1], 'generators': [109, 114, 36, 216], 'label': '648.297.18.q1.d1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.q1.d1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.q1.d1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362816
    {'ambient': '648.297', 'aut_centralizer_order': 3, 'aut_label': '18.r1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.10', 'aut_weyl_index': 108, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '9.c1.a1'], 'contains': ['36.k1.a1', '36.o1.a1', '36.s1.a1', '54.l1.a1', '54.n1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [316, -1, 1051, -1, 6628, -1, 4260, -1], 'generators': [433, 114, 4, 36], 'label': '648.297.18.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.r1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.r1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362817
    {'ambient': '648.297', 'aut_centralizer_order': 3, 'aut_label': '18.r1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.10', 'aut_weyl_index': 108, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.b1', '9.c1.a1'], 'contains': ['36.k1.a1', '36.o1.b1', '36.s1.b1', '54.l1.b1', '54.n1.b1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [316, -1, 4452, -1, 6628, -1, 4374, -1], 'generators': [1, 6, 4, 36], 'label': '648.297.18.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.r1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.r1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362818
    {'ambient': '648.297', 'aut_centralizer_order': 1, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '972.429', 'aut_weyl_index': 4, 'centralizer': '324.a1.a1', 'complements': ['324.a1.a1', '324.d1.b1', '324.b1.a1', '324.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.b1', '4.c1.b1', '4.d1.a1', '6.h1.d1', '6.i1.d1'], 'core': '2.d1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [5826, 6244, 7487, 7764, 2514, 5943, 5878, 7337], 'generators': [109, 216, 36, 114, 4, 48], 'label': '648.297.2.d1.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.d1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.b1', '4.c1.b1', '4.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.d1', 'projective_image': '648.297', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.d1.d1', 'subgroup_fusion': None, 'weyl_group': '324.37'}
  • id: 110362819
    {'ambient': '648.297', 'aut_centralizer_order': 3, 'aut_label': '18.r1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.10', 'aut_weyl_index': 108, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.c1', '9.c1.a1'], 'contains': ['36.k1.b1', '36.o1.a1', '36.s1.b1', '54.l1.c1', '54.n1.c1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [316, -1, 2696, -1, 6628, -1, 3496, -1], 'generators': [325, 6, 4, 36], 'label': '648.297.18.r1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.r1.c1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.r1.c1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362820
    {'ambient': '648.297', 'aut_centralizer_order': 3, 'aut_label': '18.r1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.10', 'aut_weyl_index': 108, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.d1', '9.c1.a1'], 'contains': ['36.k1.b1', '36.o1.b1', '36.s1.a1', '54.l1.d1', '54.n1.d1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [316, -1, 1196, -1, 6628, -1, 3381, -1], 'generators': [109, 114, 4, 36], 'label': '648.297.18.r1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.r1.d1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.r1.d1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362821
    {'ambient': '648.297', 'aut_centralizer_order': 3, 'aut_label': '18.s1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.10', 'aut_weyl_index': 108, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '9.d1.a1'], 'contains': ['36.c1.a1', '36.m1.a1', '36.r1.a1', '54.m1.a1', '54.n1.a1'], 'core': '36.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1716, -1, 3290, -1, 6447, -1, 2079, -1], 'generators': [1, 114, 4, 216], 'label': '648.297.18.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '18.s1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.s1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362822
    {'ambient': '648.297', 'aut_centralizer_order': 3, 'aut_label': '18.s1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.10', 'aut_weyl_index': 108, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.b1', '9.d1.a1'], 'contains': ['36.c1.a1', '36.m1.b1', '36.r1.b1', '54.m1.b1', '54.n1.b1'], 'core': '36.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1716, -1, 4597, -1, 6447, -1, 2193, -1], 'generators': [1, 6, 4, 216], 'label': '648.297.18.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '18.s1.b1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.s1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362823
    {'ambient': '648.297', 'aut_centralizer_order': 3, 'aut_label': '18.s1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.10', 'aut_weyl_index': 108, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.c1', '9.d1.a1'], 'contains': ['36.c1.b1', '36.m1.a1', '36.r1.b1', '54.m1.c1', '54.n1.c1'], 'core': '36.c1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [1716, -1, 3826, -1, 6447, -1, 1507, -1], 'generators': [109, 6, 4, 216], 'label': '648.297.18.s1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '18.s1.c1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.s1.c1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362824
    {'ambient': '648.297', 'aut_centralizer_order': 3, 'aut_label': '18.s1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.10', 'aut_weyl_index': 108, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.d1', '9.d1.a1'], 'contains': ['36.c1.b1', '36.m1.b1', '36.r1.a1', '54.m1.d1', '54.n1.d1'], 'core': '36.c1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [1716, -1, 2597, -1, 6447, -1, 1393, -1], 'generators': [109, 114, 4, 216], 'label': '648.297.18.s1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '18.s1.d1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.s1.d1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 110362825
    {'ambient': '648.297', 'aut_centralizer_order': 324, 'aut_label': '24.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.c1.a1', '12.c1.b1', '12.g1.a1', '12.g1.b1', '12.j1.a1', '12.j1.b1'], 'contains': ['72.a1.a1', '72.b1.a1', '72.c1.a1', '72.d1.a1', '72.g1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3337, 5634, 2163, 6145, 7588, 5679, 4237, 4088], 'generators': [4, 36, 216], 'label': '648.297.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1', '12.c1.a1', '12.c1.b1'], 'normal_contains': ['72.a1.a1', '72.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '648.297', 'quotient_action_image': '12.4', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110362826
    {'ambient': '648.297', 'aut_centralizer_order': 108, 'aut_label': '24.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '36.12', 'aut_weyl_index': 108, 'centralizer': '12.b1.a1', 'complements': ['27.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.b1.a1', '12.d1.a1', '12.d1.b1', '12.f1.a1', '12.f1.b1', '12.h1.a1', '12.h1.b1'], 'contains': ['72.a1.a1', '72.e1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7292, 2923, 9709, 4006, 1627, 3016, 7733, 6128], 'generators': [84, 216], 'label': '648.297.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.a1.a1', '12.b1.a1', '12.d1.a1', '12.d1.b1'], 'normal_contains': ['72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '648.297', 'quotient_action_image': '12.4', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110362827
    {'ambient': '648.297', 'aut_centralizer_order': 108, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '18.3', 'aut_weyl_index': 216, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.e1.a1', '12.i1.a1', '12.i1.b1'], 'contains': ['72.a1.a1', '72.f1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7813, -1, 8900, -1, 1930, -1, 9325, -1], 'generators': [88, 216], 'label': '648.297.24.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.c1.a1', 'projective_image': '648.297', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362828
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '24.14', 'aut_weyl_index': 162, 'centralizer': '162.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '9.b1.a1', '9.c1.a1'], 'contains': ['54.a1.a1', '54.e1.a1', '54.j1.a1', '54.l1.a1', '54.l1.b1', '54.l1.c1', '54.l1.d1', '81.a1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [6802, -1, 6870, -1, 3959, -1, 6445, -1], 'generators': [1, 6, 324, 36], 'label': '648.297.27.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '27.a1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362829
    {'ambient': '648.297', 'aut_centralizer_order': 1, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1296.3034', 'aut_weyl_index': 3, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.a1', '6.c1.a1', '6.e1.a1', '6.h1.a1', '6.h1.b1', '6.h1.c1', '6.h1.d1', '9.a1.a1', '9.b1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7384, -1, 7967, -1, 1623, -1, 7677, -1], 'generators': [1, 36, 216, 6, 324, 48], 'label': '648.297.3.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '108.16'}
  • id: 110362830
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '27.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '24.14', 'aut_weyl_index': 162, 'centralizer': '162.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1.a1', '9.d1.a1'], 'contains': ['54.b1.a1', '54.d1.a1', '54.i1.a1', '54.m1.a1', '54.m1.b1', '54.m1.c1', '54.m1.d1', '81.a1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4455, -1, 4287, -1, 4910, -1, 2552, -1], 'generators': [1, 6, 324, 216], 'label': '648.297.27.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '27.b1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362831
    {'ambient': '648.297', 'aut_centralizer_order': 6, 'aut_label': '27.c1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '24.14', 'aut_weyl_index': 162, 'centralizer': '162.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1.a1', '9.d1.a1'], 'contains': ['54.c1.a1', '54.f1.a1', '54.h1.a1', '54.n1.a1', '54.n1.b1', '54.n1.c1', '54.n1.d1', '81.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [554, -1, 2071, -1, 7263, -1, 1675, -1], 'generators': [1, 6, 324, 4], 'label': '648.297.27.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1.a1', 'old_label': '27.c1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362832
    {'ambient': '648.297', 'aut_centralizer_order': 972, 'aut_label': '36.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 972, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.b1.a1', '12.e1.a1', '18.c1.a1', '18.e1.a1', '18.n1.a1'], 'contains': ['72.a1.a1', '108.a1.a1', '108.b1.a1', '108.c1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7838, 4553, 6491, 3989, 3721, 4527, 6468, 4882], 'generators': [324, 36, 216], 'label': '648.297.36.a1.a1', 'mobius_quo': -1, 'mobius_sub': 18, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['12.a1.a1', '12.b1.a1'], 'normal_contains': ['72.a1.a1', '108.b1.a1', '108.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '324.37', 'quotient_action_image': '4.2', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110362833
    {'ambient': '648.297', 'aut_centralizer_order': 324, 'aut_label': '36.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '12.a1.a1', 'complements': ['18.p1.b1', '18.p1.c1', '18.p1.a1', '18.p1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.a1.a1', '18.f1.a1', '18.k1.a1'], 'contains': ['72.b1.a1', '108.a1.a1', '108.d1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2995, 6717, 3395, 5886, 8133, 6830, 1772, 3293], 'generators': [324, 4, 216], 'label': '648.297.36.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': ['12.a1.a1', '18.a1.a1'], 'normal_contains': ['72.b1.a1', '108.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.b1.a1', 'projective_image': '324.37', 'quotient_action_image': '12.4', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110362834
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '36.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '108.17', 'aut_weyl_index': 36, 'centralizer': '108.b1.a1', 'complements': ['18.o1.a1', '18.i1.a1', '18.j1.a1', '18.p1.c1', '18.p1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '18.a1.a1', '18.s1.a1', '18.s1.b1'], 'contains': ['72.b1.a1', '108.g1.a1', '108.h1.a1'], 'core': '36.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1842, 8134, 5175, 7245, 6933, 8034, 2136, 1749], 'generators': [1, 4, 216], 'label': '648.297.36.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '36.c1.a1', 'normal_contained_in': ['12.c1.a1', '18.a1.a1'], 'normal_contains': ['72.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.c1.a1', 'projective_image': '648.297', 'quotient_action_image': '6.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '36.c1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 110362835
    {'ambient': '648.297', 'aut_centralizer_order': 18, 'aut_label': '36.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '108.17', 'aut_weyl_index': 36, 'centralizer': '108.b1.a1', 'complements': ['18.o1.a1', '18.i1.a1', '18.j1.a1', '18.p1.b1', '18.p1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['12.c1.b1', '18.a1.a1', '18.s1.c1', '18.s1.d1'], 'contains': ['72.b1.a1', '108.g1.b1', '108.h1.b1'], 'core': '36.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1842, 8134, 3579, 8273, 6933, 8034, 1508, 2463], 'generators': [109, 4, 216], 'label': '648.297.36.c1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '36.c1.b1', 'normal_contained_in': ['12.c1.b1', '18.a1.a1'], 'normal_contains': ['72.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.c1.b1', 'projective_image': '648.297', 'quotient_action_image': '6.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '36.c1.b1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 110362836
    {'ambient': '648.297', 'aut_centralizer_order': 324, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.g1.a1'], 'contains': ['72.c1.a1', '108.a1.a1', '108.e1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4715, -1, 2321, -1, 9405, -1, 4905, -1], 'generators': [324, 40, 216], 'label': '648.297.36.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '36.d1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110362837
    {'ambient': '648.297', 'aut_centralizer_order': 324, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 972, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.d1.a1', '18.h1.a1', '18.l1.a1'], 'contains': ['72.d1.a1', '108.b1.a1', '108.d1.a1', '108.e1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1254, -1, 503, -1, 8436, -1, 4391, -1], 'generators': [324, 4, 36], 'label': '648.297.36.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.e1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110362838
    {'ambient': '648.297', 'aut_centralizer_order': 216, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.2', 'aut_weyl_index': 648, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.b1.a1', '18.i1.a1', '18.o1.a1'], 'contains': ['72.e1.a1', '108.b1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9944, -1, 9175, -1, 1217, -1, 8360, -1], 'generators': [324, 84, 36], 'label': '648.297.36.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.f1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110362839
    {'ambient': '648.297', 'aut_centralizer_order': 108, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 648, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.j1.a1'], 'contains': ['72.f1.a1', '108.b1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8966, -1, 7899, -1, 2179, -1, 9483, -1], 'generators': [324, 88, 36], 'label': '648.297.36.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '36.g1.a1', 'projective_image': '324.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}