Abstract group data - 1944.2466

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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': '6.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 36, 'aut_gen_orders': [12, 18, 18], 'aut_gens': [[1, 6, 18, 108], [523, 1398, 666, 1278], [1433, 1644, 990, 1170], [1531, 1392, 1314, 108]], 'aut_group': None, 'aut_hash': 7552333044196234017, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 3888, 'aut_permdeg': 56, 'aut_perms': [64610837451368868952709560986607327175621131250948329610779116395975378587, 232921748014274236942010625528359324776059203671681580091642089417649870245, 669617986692279867733805315033085225701565891026708189710219069905570550474], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 54, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 3, 1, 2], [3, 3, 2, 2], [3, 72, 1, 1], [3, 72, 2, 1], [4, 54, 1, 1], [6, 3, 2, 1], [6, 6, 1, 1], [6, 6, 2, 1], [6, 9, 1, 2], [6, 9, 2, 2], [6, 54, 1, 2], [6, 54, 2, 3], [9, 18, 1, 1], [9, 18, 2, 1], [9, 24, 3, 1], [9, 24, 6, 1], [9, 72, 1, 1], [9, 72, 2, 1], [12, 54, 1, 2], [12, 54, 2, 3], [18, 18, 1, 3], [18, 18, 2, 3]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times C_9:C_3:A_4.C_6', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 36, 'autcentquo_group': '1944.2468', 'autcentquo_hash': 2468, 'autcentquo_nilpotent': False, 'autcentquo_order': 1944, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_9:C_3^2:S_4', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 54, 1], [3, 1, 2], [3, 2, 3], [3, 3, 6], [3, 72, 3], [4, 54, 1], [6, 3, 2], [6, 6, 3], [6, 9, 6], [6, 54, 8], [9, 18, 3], [9, 24, 9], [9, 72, 3], [12, 54, 8], [18, 18, 9]], 'center_label': '3.1', 'center_order': 3, 'central_product': True, 'central_quotient': '648.278', 'commutator_count': 2, 'commutator_label': '324.57', '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', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 2466, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['648.278', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 54, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 3, 2, 3], [3, 72, 1, 1], [3, 72, 2, 1], [4, 54, 1, 1], [6, 3, 2, 1], [6, 6, 1, 1], [6, 6, 2, 1], [6, 9, 2, 3], [6, 54, 2, 4], [9, 18, 1, 1], [9, 18, 2, 1], [9, 24, 3, 1], [9, 24, 6, 1], [9, 72, 1, 1], [9, 72, 2, 1], [12, 54, 2, 4], [18, 18, 1, 1], [18, 18, 2, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 884520, 'exponent': 36, 'exponents_of_order': [5, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[18, 0, 2]], 'familial': False, 'frattini_label': '9.2', 'frattini_quotient': '216.164', 'hash': 2466, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 36, 'inner_gen_orders': [2, 3, 6, 18], 'inner_gens': [[1, 12, 18, 1278], [13, 6, 1692, 1422], [1, 384, 18, 756], [1531, 1392, 1314, 108]], 'inner_hash': 278, 'inner_nilpotent': False, 'inner_order': 648, 'inner_split': True, 'inner_tex': 'C_9:C_3:S_4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 18, 'irrQ_degree': 36, 'irrQ_dim': 36, 'irrR_degree': 36, 'irrep_stats': [[1, 6], [2, 12], [3, 30], [6, 18], [18, 3]], 'label': '1944.2466', 'linC_count': 144, 'linC_degree': 9, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 20, 'linQ_degree_count': 2, 'linQ_dim': 20, 'linQ_dim_count': 2, 'linR_count': 12, 'linR_degree': 11, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C9:C3^2:S4', 'ngens': 8, '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, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 42, 'number_characteristic_subgroups': 26, 'number_conjugacy_classes': 69, 'number_divisions': 37, 'number_normal_subgroups': 30, 'number_subgroup_autclasses': 221, 'number_subgroup_classes': 256, 'number_subgroups': 2620, 'old_label': None, 'order': 1944, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 57], [3, 242], [4, 54], [6, 510], [9, 486], [12, 432], [18, 162]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [6], 'outer_gen_pows': [0], 'outer_gens': [[5, 1302, 18, 108]], 'outer_group': '6.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 6, 'outer_permdeg': 5, 'outer_perms': [28], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 34, 'pgroup': 0, 'primary_abelian_invariants': [2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 6], [3, 2], [4, 4], [6, 15], [12, 4], [18, 2], [36, 2]], 'representations': {'PC': {'code': 188443224697509660285726738432760017065569622490838831753423211, 'gens': [1, 3, 4, 6], 'pres': [8, 2, 3, 3, 2, 3, 2, 3, 3, 16, 290, 9043, 91, 8900, 61349, 11397, 2045, 1909, 141, 64518, 14470, 4734, 1382, 222, 82951]}, 'GLZN': {'d': 2, 'p': 108, 'gens': [1895401, 69914071, 1259785, 97916017, 1263601, 91959049, 62010229, 28380433]}, 'Perm': {'d': 34, 'gens': [840854401150115000501050565366052744, 3, 9498442839985422154712511178825173264, 18478649459819593564242716314976618880, 1382047922865419991418557572381969280, 27696725857374320156899483205728070400, 744, 1680]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [6], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_9:C_3^2:S_4', 'transitive_degree': 108, '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: 136796632
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 2466, 'group_order': 1944, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 136796643
    {'aut_label': '2A', 'centralizer': '3.c1.a1', 'counter': 2, 'group_counter': 2466, 'group_order': 1944, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 972, 'size': 3}
  • id: 136796654
    {'aut_label': '2B', 'centralizer': '54.d1.a1', 'counter': 3, 'group_counter': 2466, 'group_order': 1944, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 3, 'size': 54}
  • id: 136796665
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 2466, 'group_order': 1944, 'label': '3A1', 'order': 3, 'powers': [5, 1], 'representative': 4, 'size': 1}
  • id: 136796676
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 5, 'group_counter': 2466, 'group_order': 1944, 'label': '3A-1', 'order': 3, 'powers': [4, 1], 'representative': 2, 'size': 1}
  • id: 136796687
    {'aut_label': '3B', 'centralizer': '2.a1.a1', 'counter': 6, 'group_counter': 2466, 'group_order': 1944, 'label': '3B', 'order': 3, 'powers': [6, 1], 'representative': 648, 'size': 2}
  • id: 136796698
    {'aut_label': '3C1', 'centralizer': '2.a1.a1', 'counter': 7, 'group_counter': 2466, 'group_order': 1944, 'label': '3C1', 'order': 3, 'powers': [8, 1], 'representative': 652, 'size': 2}
  • id: 136796699
    {'aut_label': '3C1', 'centralizer': '2.a1.a1', 'counter': 8, 'group_counter': 2466, 'group_order': 1944, 'label': '3C-1', 'order': 3, 'powers': [7, 1], 'representative': 1298, 'size': 2}
  • id: 136796700
    {'aut_label': '3D1', 'centralizer': '3.d1.a1', 'counter': 9, 'group_counter': 2466, 'group_order': 1944, 'label': '3D1', 'order': 3, 'powers': [10, 1], 'representative': 72, 'size': 3}
  • id: 136796633
    {'aut_label': '3D-1', 'centralizer': '3.d1.a1', 'counter': 10, 'group_counter': 2466, 'group_order': 1944, 'label': '3D-1', 'order': 3, 'powers': [9, 1], 'representative': 36, 'size': 3}
  • id: 136796634
    {'aut_label': '3E1', 'centralizer': '3.d1.a1', 'counter': 11, 'group_counter': 2466, 'group_order': 1944, 'label': '3E1', 'order': 3, 'powers': [12, 1], 'representative': 722, 'size': 3}
  • id: 136796635
    {'aut_label': '3E-1', 'centralizer': '3.d1.a1', 'counter': 12, 'group_counter': 2466, 'group_order': 1944, 'label': '3E-1', 'order': 3, 'powers': [11, 1], 'representative': 1336, 'size': 3}
  • id: 136796636
    {'aut_label': '3E-1', 'centralizer': '3.d1.a1', 'counter': 13, 'group_counter': 2466, 'group_order': 1944, 'label': '3F1', 'order': 3, 'powers': [14, 1], 'representative': 38, 'size': 3}
  • id: 136796637
    {'aut_label': '3E1', 'centralizer': '3.d1.a1', 'counter': 14, 'group_counter': 2466, 'group_order': 1944, 'label': '3F-1', 'order': 3, 'powers': [13, 1], 'representative': 76, 'size': 3}
  • id: 136796638
    {'aut_label': '3G', 'centralizer': '72.c1.a1', 'counter': 15, 'group_counter': 2466, 'group_order': 1944, 'label': '3G', 'order': 3, 'powers': [15, 1], 'representative': 78, 'size': 72}
  • id: 136796639
    {'aut_label': '3H1', 'centralizer': '72.c1.a1', 'counter': 16, 'group_counter': 2466, 'group_order': 1944, 'label': '3H1', 'order': 3, 'powers': [17, 1], 'representative': 680, 'size': 72}
  • id: 136796640
    {'aut_label': '3H1', 'centralizer': '72.c1.a1', 'counter': 17, 'group_counter': 2466, 'group_order': 1944, 'label': '3H-1', 'order': 3, 'powers': [16, 1], 'representative': 1666, 'size': 72}
  • id: 136796641
    {'aut_label': '4A', 'centralizer': '54.j1.a1', 'counter': 18, 'group_counter': 2466, 'group_order': 1944, 'label': '4A', 'order': 4, 'powers': [2, 18], 'representative': 69, 'size': 54}
  • id: 136796642
    {'aut_label': '6A1', 'centralizer': '3.c1.a1', 'counter': 19, 'group_counter': 2466, 'group_order': 1944, 'label': '6A1', 'order': 6, 'powers': [4, 2], 'representative': 56, 'size': 3}
  • id: 136796644
    {'aut_label': '6A1', 'centralizer': '3.c1.a1', 'counter': 20, 'group_counter': 2466, 'group_order': 1944, 'label': '6A-1', 'order': 6, 'powers': [5, 2], 'representative': 58, 'size': 3}
  • id: 136796645
    {'aut_label': '6B', 'centralizer': '6.b1.a1', 'counter': 21, 'group_counter': 2466, 'group_order': 1944, 'label': '6B', 'order': 6, 'powers': [6, 2], 'representative': 324, 'size': 6}
  • id: 136796646
    {'aut_label': '6C1', 'centralizer': '6.b1.a1', 'counter': 22, 'group_counter': 2466, 'group_order': 1944, 'label': '6C1', 'order': 6, 'powers': [7, 2], 'representative': 326, 'size': 6}
  • id: 136796647
    {'aut_label': '6C1', 'centralizer': '6.b1.a1', 'counter': 23, 'group_counter': 2466, 'group_order': 1944, 'label': '6C-1', 'order': 6, 'powers': [8, 2], 'representative': 328, 'size': 6}
  • id: 136796648
    {'aut_label': '6D1', 'centralizer': '9.a1.a1', 'counter': 24, 'group_counter': 2466, 'group_order': 1944, 'label': '6D1', 'order': 6, 'powers': [11, 2], 'representative': 364, 'size': 9}
  • id: 136796649
    {'aut_label': '6D-1', 'centralizer': '9.a1.a1', 'counter': 25, 'group_counter': 2466, 'group_order': 1944, 'label': '6D-1', 'order': 6, 'powers': [12, 2], 'representative': 1694, 'size': 9}
  • id: 136796650
    {'aut_label': '6D-1', 'centralizer': '9.a1.a1', 'counter': 26, 'group_counter': 2466, 'group_order': 1944, 'label': '6E1', 'order': 6, 'powers': [13, 2], 'representative': 22, 'size': 9}
  • id: 136796651
    {'aut_label': '6D1', 'centralizer': '9.a1.a1', 'counter': 27, 'group_counter': 2466, 'group_order': 1944, 'label': '6E-1', 'order': 6, 'powers': [14, 2], 'representative': 92, 'size': 9}
  • id: 136796652
    {'aut_label': '6F1', 'centralizer': '9.a1.a1', 'counter': 28, 'group_counter': 2466, 'group_order': 1944, 'label': '6F1', 'order': 6, 'powers': [10, 2], 'representative': 1638, 'size': 9}
  • id: 136796653
    {'aut_label': '6F-1', 'centralizer': '9.a1.a1', 'counter': 29, 'group_counter': 2466, 'group_order': 1944, 'label': '6F-1', 'order': 6, 'powers': [9, 2], 'representative': 414, 'size': 9}
  • id: 136796655
    {'aut_label': '6G1', 'centralizer': '54.d1.a1', 'counter': 30, 'group_counter': 2466, 'group_order': 1944, 'label': '6G1', 'order': 6, 'powers': [9, 3], 'representative': 39, 'size': 54}
  • id: 136796656
    {'aut_label': '6G-1', 'centralizer': '54.d1.a1', 'counter': 31, 'group_counter': 2466, 'group_order': 1944, 'label': '6G-1', 'order': 6, 'powers': [10, 3], 'representative': 75, 'size': 54}
  • id: 136796657
    {'aut_label': '6H1', 'centralizer': '54.d1.a1', 'counter': 32, 'group_counter': 2466, 'group_order': 1944, 'label': '6H1', 'order': 6, 'powers': [12, 3], 'representative': 1709, 'size': 54}
  • id: 136796658
    {'aut_label': '6H-1', 'centralizer': '54.d1.a1', 'counter': 33, 'group_counter': 2466, 'group_order': 1944, 'label': '6H-1', 'order': 6, 'powers': [11, 3], 'representative': 373, 'size': 54}
  • id: 136796659
    {'aut_label': '6I1', 'centralizer': '54.d1.a1', 'counter': 34, 'group_counter': 2466, 'group_order': 1944, 'label': '6I1', 'order': 6, 'powers': [4, 3], 'representative': 125, 'size': 54}
  • id: 136796660
    {'aut_label': '6I1', 'centralizer': '54.d1.a1', 'counter': 35, 'group_counter': 2466, 'group_order': 1944, 'label': '6I-1', 'order': 6, 'powers': [5, 3], 'representative': 121, 'size': 54}
  • id: 136796661
    {'aut_label': '6H1', 'centralizer': '54.d1.a1', 'counter': 36, 'group_counter': 2466, 'group_order': 1944, 'label': '6J1', 'order': 6, 'powers': [13, 3], 'representative': 1519, 'size': 54}
  • id: 136796662
    {'aut_label': '6H-1', 'centralizer': '54.d1.a1', 'counter': 37, 'group_counter': 2466, 'group_order': 1944, 'label': '6J-1', 'order': 6, 'powers': [14, 3], 'representative': 1595, 'size': 54}
  • id: 136796663
    {'aut_label': '9A', 'centralizer': '18.o1.a1', 'counter': 38, 'group_counter': 2466, 'group_order': 1944, 'label': '9A', 'order': 9, 'powers': [38, 6], 'representative': 216, 'size': 18}
  • id: 136796664
    {'aut_label': '9B1', 'centralizer': '18.o1.a1', 'counter': 39, 'group_counter': 2466, 'group_order': 1944, 'label': '9B1', 'order': 9, 'powers': [40, 6], 'representative': 220, 'size': 18}
  • id: 136796666
    {'aut_label': '9B1', 'centralizer': '18.o1.a1', 'counter': 40, 'group_counter': 2466, 'group_order': 1944, 'label': '9B-1', 'order': 9, 'powers': [39, 6], 'representative': 1730, 'size': 18}
  • id: 136796667
    {'aut_label': '9C1', 'centralizer': '24.c1.a1', 'counter': 41, 'group_counter': 2466, 'group_order': 1944, 'label': '9C1', 'order': 9, 'powers': [42, 6], 'representative': 114, 'size': 24}
  • id: 136796668
    {'aut_label': '9C1', 'centralizer': '24.c1.a1', 'counter': 42, 'group_counter': 2466, 'group_order': 1944, 'label': '9C2', 'order': 9, 'powers': [43, 6], 'representative': 438, 'size': 24}
  • id: 136796669
    {'aut_label': '9C1', 'centralizer': '24.c1.a1', 'counter': 43, 'group_counter': 2466, 'group_order': 1944, 'label': '9C4', 'order': 9, 'powers': [41, 6], 'representative': 228, 'size': 24}
  • id: 136796670
    {'aut_label': '9D1', 'centralizer': '24.c1.a1', 'counter': 44, 'group_counter': 2466, 'group_order': 1944, 'label': '9D1', 'order': 9, 'powers': [46, 6], 'representative': 116, 'size': 24}
  • id: 136796671
    {'aut_label': '9D1', 'centralizer': '24.c1.a1', 'counter': 45, 'group_counter': 2466, 'group_order': 1944, 'label': '9D-1', 'order': 9, 'powers': [47, 6], 'representative': 118, 'size': 24}
  • id: 136796672
    {'aut_label': '9D1', 'centralizer': '24.c1.a1', 'counter': 46, 'group_counter': 2466, 'group_order': 1944, 'label': '9D2', 'order': 9, 'powers': [48, 6], 'representative': 442, 'size': 24}
  • id: 136796673
    {'aut_label': '9D1', 'centralizer': '24.c1.a1', 'counter': 47, 'group_counter': 2466, 'group_order': 1944, 'label': '9D-2', 'order': 9, 'powers': [49, 6], 'representative': 440, 'size': 24}
  • id: 136796674
    {'aut_label': '9D1', 'centralizer': '24.c1.a1', 'counter': 48, 'group_counter': 2466, 'group_order': 1944, 'label': '9D4', 'order': 9, 'powers': [45, 6], 'representative': 230, 'size': 24}
  • id: 136796675
    {'aut_label': '9D1', 'centralizer': '24.c1.a1', 'counter': 49, 'group_counter': 2466, 'group_order': 1944, 'label': '9D-4', 'order': 9, 'powers': [44, 6], 'representative': 232, 'size': 24}
  • id: 136796677
    {'aut_label': '9E', 'centralizer': '72.f1.a1', 'counter': 50, 'group_counter': 2466, 'group_order': 1944, 'label': '9E', 'order': 9, 'powers': [50, 6], 'representative': 1860, 'size': 72}
  • id: 136796678
    {'aut_label': '9F1', 'centralizer': '72.f1.a1', 'counter': 51, 'group_counter': 2466, 'group_order': 1944, 'label': '9F1', 'order': 9, 'powers': [52, 6], 'representative': 1510, 'size': 72}
  • id: 136796679
    {'aut_label': '9F1', 'centralizer': '72.f1.a1', 'counter': 52, 'group_counter': 2466, 'group_order': 1944, 'label': '9F-1', 'order': 9, 'powers': [51, 6], 'representative': 926, 'size': 72}
  • id: 136796680
    {'aut_label': '12A1', 'centralizer': '54.j1.a1', 'counter': 53, 'group_counter': 2466, 'group_order': 1944, 'label': '12A1', 'order': 12, 'powers': [24, 18], 'representative': 1655, 'size': 54}
  • id: 136796681
    {'aut_label': '12A-1', 'centralizer': '54.j1.a1', 'counter': 54, 'group_counter': 2466, 'group_order': 1944, 'label': '12A-1', 'order': 12, 'powers': [25, 18], 'representative': 1399, 'size': 54}
  • id: 136796682
    {'aut_label': '12A-1', 'centralizer': '54.j1.a1', 'counter': 55, 'group_counter': 2466, 'group_order': 1944, 'label': '12B1', 'order': 12, 'powers': [26, 18], 'representative': 1715, 'size': 54}
  • id: 136796683
    {'aut_label': '12A1', 'centralizer': '54.j1.a1', 'counter': 56, 'group_counter': 2466, 'group_order': 1944, 'label': '12B-1', 'order': 12, 'powers': [27, 18], 'representative': 1693, 'size': 54}
  • id: 136796684
    {'aut_label': '12C1', 'centralizer': '54.j1.a1', 'counter': 57, 'group_counter': 2466, 'group_order': 1944, 'label': '12C1', 'order': 12, 'powers': [19, 18], 'representative': 1207, 'size': 54}
  • id: 136796685
    {'aut_label': '12C1', 'centralizer': '54.j1.a1', 'counter': 58, 'group_counter': 2466, 'group_order': 1944, 'label': '12C-1', 'order': 12, 'powers': [20, 18], 'representative': 1265, 'size': 54}
  • id: 136796686
    {'aut_label': '12D1', 'centralizer': '54.j1.a1', 'counter': 59, 'group_counter': 2466, 'group_order': 1944, 'label': '12D1', 'order': 12, 'powers': [28, 18], 'representative': 891, 'size': 54}
  • id: 136796688
    {'aut_label': '12D-1', 'centralizer': '54.j1.a1', 'counter': 60, 'group_counter': 2466, 'group_order': 1944, 'label': '12D-1', 'order': 12, 'powers': [29, 18], 'representative': 1845, 'size': 54}
  • id: 136796689
    {'aut_label': '18A', 'centralizer': '18.o1.a1', 'counter': 61, 'group_counter': 2466, 'group_order': 1944, 'label': '18A', 'order': 18, 'powers': [38, 21], 'representative': 108, 'size': 18}
  • id: 136796690
    {'aut_label': '18B1', 'centralizer': '18.o1.a1', 'counter': 62, 'group_counter': 2466, 'group_order': 1944, 'label': '18B1', 'order': 18, 'powers': [38, 21], 'representative': 144, 'size': 18}
  • id: 136796691
    {'aut_label': '18B-1', 'centralizer': '18.o1.a1', 'counter': 63, 'group_counter': 2466, 'group_order': 1944, 'label': '18B-1', 'order': 18, 'powers': [38, 21], 'representative': 180, 'size': 18}
  • id: 136796692
    {'aut_label': '18C1', 'centralizer': '18.o1.a1', 'counter': 64, 'group_counter': 2466, 'group_order': 1944, 'label': '18C1', 'order': 18, 'powers': [39, 21], 'representative': 110, 'size': 18}
  • id: 136796693
    {'aut_label': '18C1', 'centralizer': '18.o1.a1', 'counter': 65, 'group_counter': 2466, 'group_order': 1944, 'label': '18C-1', 'order': 18, 'powers': [40, 21], 'representative': 112, 'size': 18}
  • id: 136796694
    {'aut_label': '18D1', 'centralizer': '18.o1.a1', 'counter': 66, 'group_counter': 2466, 'group_order': 1944, 'label': '18D1', 'order': 18, 'powers': [39, 21], 'representative': 146, 'size': 18}
  • id: 136796695
    {'aut_label': '18D-1', 'centralizer': '18.o1.a1', 'counter': 67, 'group_counter': 2466, 'group_order': 1944, 'label': '18D-1', 'order': 18, 'powers': [40, 21], 'representative': 184, 'size': 18}
  • id: 136796696
    {'aut_label': '18D-1', 'centralizer': '18.o1.a1', 'counter': 68, 'group_counter': 2466, 'group_order': 1944, 'label': '18E1', 'order': 18, 'powers': [39, 21], 'representative': 182, 'size': 18}
  • id: 136796697
    {'aut_label': '18D1', 'centralizer': '18.o1.a1', 'counter': 69, 'group_counter': 2466, 'group_order': 1944, 'label': '18E-1', 'order': 18, 'powers': [40, 21], 'representative': 148, '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: 12036707
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.1a', '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, 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: 12036718
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.1b', '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, 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: 12036729
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.1c', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, 2, -1, 2, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, 2, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1], 'schur_index': 1}
  • id: 12036738
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.1d', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, 2, -1, -2, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, 2, 1, 1, -2, 1, 1, -2, 1, 1, 2, -1, -1, 2, -1, 2, -1, -1, 2, -1, -1, -1, 2, -1, -1, 1, 1, 1, -2, 1, 1, -2, 1, 2, 2, -1, -1, -1, -1, -1, 2, -1], 'schur_index': 1}
  • id: 12036739
    {'cdim': 2, 'counter': 5, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12036740
    {'cdim': 2, 'counter': 6, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12036741
    {'cdim': 2, 'counter': 7, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.2c', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'schur_index': 1}
  • id: 12036742
    {'cdim': 2, 'counter': 8, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.2d', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12036711
    {'cdim': 3, 'counter': 13, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, -1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12036712
    {'cdim': 3, 'counter': 14, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.3b', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, -1, -1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12036743
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.2e', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 0, -2, -2, 4, -2, -2, -2, -2, -2, 4, 4, -2, -2, 4, -2, 0, -2, -2, -2, -2, 4, -2, 4, -2, -2, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, -2, 1, -2, 1, 1, -2, 1, 1, 1, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 1, 1, 1, 1, -2, 1], 'schur_index': 1}
  • id: 12036708
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.2f', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 0, -2, -2, 4, -2, -2, -2, -2, -2, 4, 4, -2, 1, -2, 1, 0, -2, -2, -2, -2, 4, -2, 4, -2, -2, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, -2, 1, -2, 1, 1, -2, 1, 1, 1, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 1, 1, 1, 1, -2, 1], 'schur_index': 1}
  • id: 12036709
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.2g', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 0, -2, -2, 4, -2, -2, -2, -2, -2, 4, 4, -2, 1, -2, 1, 0, -2, -2, -2, -2, 4, -2, 4, -2, -2, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, 4, -2, 4, -2, -2, 4, -2, -2, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 1, 1, 1, 1, -2, 1], 'schur_index': 1}
  • id: 12036710
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.2h', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 0, -2, -2, 4, -2, -2, -2, -2, -2, 4, 4, -2, 1, -2, 1, 0, -2, -2, -2, -2, 4, -2, 4, -2, -2, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, -2, 1, -2, 1, 1, -2, 1, 1, 1, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -2, -2, -2, -2, -2, 4, -2], 'schur_index': 1}
  • id: 12036713
    {'cdim': 3, 'counter': 15, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.3c', 'multiplicity': 2, 'nt': [9, 12], 'qdim': 6, 'qvalues': [6, 6, 2, -3, -3, 6, -3, -3, -3, 6, 6, -3, -3, -3, 0, 0, 0, 2, -3, -3, -3, -3, 6, 6, -3, -3, 6, -3, -3, -1, -1, -1, -1, 2, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -1, -1, -1, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12036714
    {'cdim': 3, 'counter': 16, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.3d', 'multiplicity': 2, 'nt': [9, 12], 'qdim': 6, 'qvalues': [6, 6, 2, -3, -3, 6, -3, -3, 6, -3, -3, -3, -3, 6, 0, 0, 0, 2, -3, -3, -3, -3, 6, -3, -3, 6, -3, 6, -3, -1, 2, -1, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 2, -1, -1, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12036715
    {'cdim': 3, 'counter': 17, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.3e', 'multiplicity': 2, 'nt': [9, 12], 'qdim': 6, 'qvalues': [6, 6, 2, 6, 6, 6, 6, 6, -3, -3, -3, -3, -3, -3, 0, 0, 0, 2, 6, 6, 6, 6, 6, -3, -3, -3, -3, -3, -3, 2, -1, -1, -1, -1, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, -1, -1, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12036716
    {'cdim': 3, 'counter': 18, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.3f', 'multiplicity': 2, 'nt': [12, 45], 'qdim': 6, 'qvalues': [6, -2, 2, -3, -3, 6, -3, -3, -3, -3, -3, 6, 6, -3, 0, 0, 0, -2, 1, 1, 1, 1, -2, 1, -2, 1, 1, 1, -2, -1, -1, 2, -1, -1, 2, -1, -1, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, -2, 1, 1, -2, 1, -2, -2, 1, 1, 1, 1, 1, -2, 1], 'schur_index': 1}
  • id: 12036717
    {'cdim': 3, 'counter': 19, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.3g', 'multiplicity': 2, 'nt': [18, 24], 'qdim': 6, 'qvalues': [6, 6, -2, -3, -3, 6, -3, -3, -3, 6, 6, -3, -3, -3, 0, 0, 0, -2, -3, -3, -3, -3, 6, 6, -3, -3, 6, -3, -3, 1, 1, 1, 1, -2, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 1, 1, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12036719
    {'cdim': 3, 'counter': 20, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.3h', 'multiplicity': 2, 'nt': [18, 24], 'qdim': 6, 'qvalues': [6, 6, -2, -3, -3, 6, -3, -3, 6, -3, -3, -3, -3, 6, 0, 0, 0, -2, -3, -3, -3, -3, 6, -3, -3, 6, -3, 6, -3, 1, -2, 1, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, 1, 1, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12036720
    {'cdim': 3, 'counter': 21, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.3i', 'multiplicity': 2, 'nt': [18, 24], 'qdim': 6, 'qvalues': [6, 6, -2, 6, 6, 6, 6, 6, -3, -3, -3, -3, -3, -3, 0, 0, 0, -2, 6, 6, 6, 6, 6, -3, -3, -3, -3, -3, -3, -2, 1, 1, 1, 1, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, 1, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12036721
    {'cdim': 3, 'counter': 22, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.3j', 'multiplicity': 2, 'nt': [18, 30], 'qdim': 6, 'qvalues': [6, -2, -2, -3, -3, 6, -3, -3, -3, -3, -3, 6, 6, -3, 0, 0, 0, 2, 1, 1, 1, 1, -2, 1, -2, 1, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 2, -1, -1, 2, -1, -2, -2, 1, 1, 1, 1, 1, -2, 1], 'schur_index': 1}
  • id: 12036722
    {'cdim': 3, 'counter': 23, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.3k', 'multiplicity': 2, 'nt': [18, 107], 'qdim': 6, 'qvalues': [6, -2, -2, -3, -3, 6, -3, -3, -3, 6, 6, -3, -3, -3, 0, 0, 0, 2, 1, 1, 1, 1, -2, -2, 1, 1, -2, 1, 1, 1, 1, 1, 1, -2, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -1, -1, -1, -1, -1, 2, 4, -2, 4, -2, -2, -2, 4, -2, -2], 'schur_index': 1}
  • id: 12036723
    {'cdim': 3, 'counter': 24, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.3l', 'multiplicity': 2, 'nt': [18, 107], 'qdim': 6, 'qvalues': [6, -2, -2, -3, -3, 6, -3, -3, 6, -3, -3, -3, -3, 6, 0, 0, 0, 2, 1, 1, 1, 1, -2, 1, 1, -2, 1, -2, 1, 1, -2, 1, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 2, -1, -1, 2, -1, -1, 4, -2, -2, -2, 4, -2, -2, -2, 4], 'schur_index': 1}
  • id: 12036724
    {'cdim': 3, 'counter': 25, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.3m', 'multiplicity': 2, 'nt': [18, 107], 'qdim': 6, 'qvalues': [6, -2, -2, 6, 6, 6, 6, 6, -3, -3, -3, -3, -3, -3, 0, 0, 0, 2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, -1, -1, 2, -1, -1, -1, 4, -2, -2, 4, -2, 4, -2, -2, -2], 'schur_index': 1}
  • id: 12036725
    {'cdim': 3, 'counter': 26, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.3n', 'multiplicity': 2, 'nt': [18, 108], 'qdim': 6, 'qvalues': [6, -2, 2, -3, -3, 6, -3, -3, -3, 6, 6, -3, -3, -3, 0, 0, 0, -2, 1, 1, 1, 1, -2, -2, 1, 1, -2, 1, 1, -1, -1, -1, -1, 2, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 1, 1, 1, 1, -2, 4, -2, 4, -2, -2, -2, 4, -2, -2], 'schur_index': 1}
  • id: 12036726
    {'cdim': 3, 'counter': 27, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.3o', 'multiplicity': 2, 'nt': [18, 108], 'qdim': 6, 'qvalues': [6, -2, 2, -3, -3, 6, -3, -3, 6, -3, -3, -3, -3, 6, 0, 0, 0, -2, 1, 1, 1, 1, -2, 1, 1, -2, 1, -2, 1, -1, 2, -1, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, 1, 1, -2, 1, 1, 4, -2, -2, -2, 4, -2, -2, -2, 4], 'schur_index': 1}
  • id: 12036727
    {'cdim': 3, 'counter': 28, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.3p', 'multiplicity': 2, 'nt': [18, 108], 'qdim': 6, 'qvalues': [6, -2, 2, 6, 6, 6, 6, 6, -3, -3, -3, -3, -3, -3, 0, 0, 0, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 2, -1, -1, -1, -1, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, 1, -2, 1, 1, 1, 4, -2, -2, 4, -2, 4, -2, -2, -2], 'schur_index': 1}
  • id: 12036728
    {'cdim': 6, 'counter': 29, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.6a', 'multiplicity': 1, 'nt': [12, 44], 'qdim': 6, 'qvalues': [6, -2, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12036730
    {'cdim': 6, 'counter': 30, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.6b', 'multiplicity': 2, 'nt': [24, 564], 'qdim': 12, 'qvalues': [12, -4, 0, -6, -6, 12, -6, -6, -6, -6, -6, 12, 12, -6, 0, 0, 0, 0, 2, 2, 2, 2, -4, 2, -4, 2, 2, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -1, -1, -1, -1, -1, 2, -1], 'schur_index': 1}
  • id: 12036731
    {'cdim': 6, 'counter': 31, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.6c', 'multiplicity': 2, 'nt': [36, 198], 'qdim': 12, 'qvalues': [12, -4, 0, -6, -6, 12, -6, -6, -6, 12, 12, -6, -6, -6, 0, 0, 0, 0, 2, 2, 2, 2, -4, -4, 2, 2, -4, 2, 2, 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, -4, 2, -4, 2, 2, 2, -4, 2, 2], 'schur_index': 1}
  • id: 12036732
    {'cdim': 6, 'counter': 32, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.6d', 'multiplicity': 2, 'nt': [36, 198], 'qdim': 12, 'qvalues': [12, -4, 0, -6, -6, 12, -6, -6, 12, -6, -6, -6, -6, 12, 0, 0, 0, 0, 2, 2, 2, 2, -4, 2, 2, -4, 2, -4, 2, 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, -4, 2, 2, 2, -4, 2, 2, 2, -4], 'schur_index': 1}
  • id: 12036733
    {'cdim': 6, 'counter': 33, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.6e', 'multiplicity': 2, 'nt': [36, 198], 'qdim': 12, 'qvalues': [12, -4, 0, 12, 12, 12, 12, 12, -6, -6, -6, -6, -6, -6, 0, 0, 0, 0, -4, -4, -4, -4, -4, 2, 2, 2, 2, 2, 2, 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, -4, 2, 2, -4, 2, -4, 2, 2, 2], 'schur_index': 1}
  • id: 12036734
    {'cdim': 6, 'counter': 34, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.6f', 'multiplicity': 3, 'nt': [27, 42], 'qdim': 18, 'qvalues': [18, 18, 0, 18, 18, -9, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 18, -9, -9, -9, 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], 'schur_index': 1}
  • id: 12036736
    {'cdim': 18, 'counter': 36, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.18a', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, -6, 0, 18, 18, -9, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -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, 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: 12036735
    {'cdim': 6, 'counter': 35, 'faithful': False, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.6g', 'multiplicity': 6, 'nt': [54, 0], 'qdim': 36, 'qvalues': [36, 36, 0, -18, -18, -18, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18, -18, 9, 9, -18, 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], 'schur_index': 1}
  • id: 12036737
    {'cdim': 18, 'counter': 37, 'faithful': True, 'group': '1944.2466', 'group_order': 1944, 'image': None, 'label': '1944.2466.18b', 'multiplicity': 2, 'nt': [108, 0], 'qdim': 36, 'qvalues': [36, -12, 0, -18, -18, -18, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, -3, -3, 6, 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], '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: 27525527
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 1944, 'label': '1944.2466.1a', '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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 27525538
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 972, 'label': '1944.2466.1b', '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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 27525549
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 3, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 648, 'label': '1944.2466.1c1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]]]}
  • id: 27525560
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 4, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 648, 'label': '1944.2466.1c2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]]]}
  • id: 27525571
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 5, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1.a1', 'kernel_order': 324, 'label': '1944.2466.1d1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]]]}
  • id: 27525582
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1.a1', 'kernel_order': 324, 'label': '1944.2466.1d2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]]]}
  • id: 27525593
    {'center': '6.d1.a1', 'center_index': 6, 'center_order': 324, 'counter': 7, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.d1.a1', 'kernel_order': 324, 'label': '1944.2466.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 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]], [[-1, 0]], [[-1, 0]], [[-1, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]]]}
  • id: 27525594
    {'center': '6.c1.a1', 'center_index': 6, 'center_order': 324, 'counter': 8, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.c1.a1', 'kernel_order': 324, 'label': '1944.2466.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 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]], [[-1, 0]], [[-1, 0]], [[-1, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 27525595
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 324, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.b1.a1', 'kernel_order': 324, 'label': '1944.2466.2c', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 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]], [[-1, 0]], [[-1, 0]], [[-1, 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]], [[0, 0]], [[0, 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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]]]}
  • id: 27525528
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 324, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 324, 'label': '1944.2466.2d', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 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]], [[2, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]]]}
  • id: 27525529
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 324, 'counter': 11, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1.a1', 'kernel_order': 108, 'label': '1944.2466.2e1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 0]], [[2, 1]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, -1]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]]]}
  • id: 27525530
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 324, 'counter': 12, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1.a1', 'kernel_order': 108, 'label': '1944.2466.2e2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, 0]], [[2, -1]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 1]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]]]}
  • id: 27525531
    {'center': '6.d1.a1', 'center_index': 6, 'center_order': 324, 'counter': 13, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.e1.a1', 'kernel_order': 108, 'label': '1944.2466.2f1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 0]], [[2, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, -1]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[2, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]]]}
  • id: 27525532
    {'center': '6.d1.a1', 'center_index': 6, 'center_order': 324, 'counter': 14, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.e1.a1', 'kernel_order': 108, 'label': '1944.2466.2f2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[2, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 1]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[2, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]]]}
  • id: 27525533
    {'center': '6.c1.a1', 'center_index': 6, 'center_order': 324, 'counter': 15, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.d1.a1', 'kernel_order': 108, 'label': '1944.2466.2g1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 0]], [[2, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, -1]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[2, 1]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]]]}
  • id: 27525534
    {'center': '6.c1.a1', 'center_index': 6, 'center_order': 324, 'counter': 16, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.d1.a1', 'kernel_order': 108, 'label': '1944.2466.2g2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[2, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 1]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 0]], [[2, -1]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]]]}
  • id: 27525535
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 324, 'counter': 17, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1.a1', 'kernel_order': 108, 'label': '1944.2466.2h1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 0]], [[2, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, -1]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 1]]]}
  • id: 27525536
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 324, 'counter': 18, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1.a1', 'kernel_order': 108, 'label': '1944.2466.2h2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[2, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 1]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, -1]]]}
  • id: 27525537
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 81, 'counter': 19, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 81, 'label': '1944.2466.3a', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 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]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 27525539
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 81, 'counter': 20, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 81, 'label': '1944.2466.3b', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 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]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 27525540
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 108, 'counter': 21, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '54.8', 'image_order': 54, 'indicator': 0, 'kernel': '54.c1.a1', 'kernel_order': 36, 'label': '1944.2466.3c1', 'nt': [9, 12], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, -1]], [[3, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 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]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27525541
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 108, 'counter': 22, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '54.8', 'image_order': 54, 'indicator': 0, 'kernel': '54.c1.a1', 'kernel_order': 36, 'label': '1944.2466.3c2', 'nt': [9, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 1]], [[3, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -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]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27525542
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 108, 'counter': 23, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '54.8', 'image_order': 54, 'indicator': 0, 'kernel': '54.c1.b1', 'kernel_order': 36, 'label': '1944.2466.3d1', 'nt': [9, 12], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 1]], [[3, 1]], [[3, 0]], [[3, -1]], [[3, 0]], [[3, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 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]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27525543
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 108, 'counter': 24, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '54.8', 'image_order': 54, 'indicator': 0, 'kernel': '54.c1.b1', 'kernel_order': 36, 'label': '1944.2466.3d2', 'nt': [9, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, -1]], [[3, -1]], [[3, 0]], [[3, 1]], [[3, 0]], [[3, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -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]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27525544
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 108, 'counter': 25, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '54.8', 'image_order': 54, 'indicator': 0, 'kernel': '54.a1.a1', 'kernel_order': 36, 'label': '1944.2466.3e1', 'nt': [9, 12], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[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]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27525545
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 108, 'counter': 26, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '54.8', 'image_order': 54, 'indicator': 0, 'kernel': '54.a1.a1', 'kernel_order': 36, 'label': '1944.2466.3e2', 'nt': [9, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[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]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27525546
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 81, 'counter': 27, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '72.42', 'image_order': 72, 'indicator': 0, 'kernel': '72.b1.a1', 'kernel_order': 27, 'label': '1944.2466.3f1', 'nt': [12, 45], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[3, 0]], [[3, -1]], [[3, 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]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]]]}
  • id: 27525547
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 81, 'counter': 28, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '72.42', 'image_order': 72, 'indicator': 0, 'kernel': '72.b1.a1', 'kernel_order': 27, 'label': '1944.2466.3f2', 'nt': [12, 2], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[3, 0]], [[3, 1]], [[3, -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]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]]]}
  • id: 27525548
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 108, 'counter': 29, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '54.8', 'image_order': 54, 'indicator': 0, 'kernel': '54.c1.a1', 'kernel_order': 36, 'label': '1944.2466.3g1', 'nt': [18, 24], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, -1]], [[3, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 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]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27525550
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 108, 'counter': 30, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '54.8', 'image_order': 54, 'indicator': 0, 'kernel': '54.c1.a1', 'kernel_order': 36, 'label': '1944.2466.3g2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 1]], [[3, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -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]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27525551
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 108, 'counter': 31, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '54.8', 'image_order': 54, 'indicator': 0, 'kernel': '54.c1.b1', 'kernel_order': 36, 'label': '1944.2466.3h1', 'nt': [18, 24], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 1]], [[3, 1]], [[3, 0]], [[3, -1]], [[3, 0]], [[3, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 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]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27525552
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  • id: 27525553
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  • id: 27525554
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  • id: 27525555
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  • id: 27525556
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  • id: 27525557
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  • id: 27525558
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  • id: 27525559
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  • id: 27525561
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  • id: 27525562
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  • id: 27525563
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  • id: 27525564
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  • id: 27525565
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  • id: 27525566
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  • id: 27525567
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 27, 'counter': 46, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '216.95', 'image_order': 216, 'indicator': 0, 'kernel': '216.c1.b1', 'kernel_order': 9, 'label': '1944.2466.3o2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -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]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, 1]], [[2, 0]]]}
  • id: 27525568
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  • id: 27525569
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 27, 'counter': 48, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '216.95', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.a1', 'kernel_order': 9, 'label': '1944.2466.3p2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[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]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 1]]]}
  • id: 27525570
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  • id: 27525572
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  • id: 27525573
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  • id: 27525574
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 27, 'counter': 52, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '216.95', 'image_order': 216, 'indicator': 0, 'kernel': '216.c1.a1', 'kernel_order': 9, 'label': '1944.2466.6c1', 'nt': [36, 198], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[6, 0]], [[6, -1]], [[6, 1]], [[6, -1]], [[6, 0]], [[6, 0]], [[6, 1]], [[6, -1]], [[6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[-2, 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, 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]], [[-2, 0]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[-2, -1]]]}
  • id: 27525575
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 27, 'counter': 53, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '216.95', 'image_order': 216, 'indicator': 0, 'kernel': '216.c1.a1', 'kernel_order': 9, 'label': '1944.2466.6c2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[6, 0]], [[6, 1]], [[6, -1]], [[6, 1]], [[6, 0]], [[6, 0]], [[6, -1]], [[6, 1]], [[6, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[-2, -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, 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]], [[-2, 0]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[-2, 1]]]}
  • id: 27525576
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 27, 'counter': 54, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '216.95', 'image_order': 216, 'indicator': 0, 'kernel': '216.c1.b1', 'kernel_order': 9, 'label': '1944.2466.6d1', 'nt': [36, 198], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[6, 0]], [[6, -1]], [[6, 1]], [[6, 0]], [[6, 1]], [[6, -1]], [[6, -1]], [[6, 1]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[-2, 0]], [[-2, -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, 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]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[-2, -1]], [[-2, -1]], [[-2, 0]]]}
  • id: 27525577
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 27, 'counter': 55, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '216.95', 'image_order': 216, 'indicator': 0, 'kernel': '216.c1.b1', 'kernel_order': 9, 'label': '1944.2466.6d2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[6, 0]], [[6, 1]], [[6, -1]], [[6, 0]], [[6, -1]], [[6, 1]], [[6, 1]], [[6, -1]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[-2, 0]], [[-2, 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, 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]], [[-2, 0]], [[-2, -1]], [[-2, -1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 0]]]}
  • id: 27525578
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 27, 'counter': 56, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '216.95', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.a1', 'kernel_order': 9, 'label': '1944.2466.6e1', 'nt': [36, 198], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, -1]], [[6, -1]], [[6, 1]], [[6, -1]], [[6, 1]], [[6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -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, 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]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]]]}
  • id: 27525579
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 27, 'counter': 57, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '216.95', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.a1', 'kernel_order': 9, 'label': '1944.2466.6e2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 1]], [[6, 1]], [[6, -1]], [[6, 1]], [[6, -1]], [[6, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 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, 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]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]]]}
  • id: 27525580
    {'center': '162.a1.a1', 'center_index': 162, 'center_order': 12, 'counter': 58, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '162.20', 'image_order': 162, 'indicator': 1, 'kernel': '162.a1.a1', 'kernel_order': 12, 'label': '1944.2466.6f1', 'nt': [27, 42], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 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]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[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: 27525581
    {'center': '162.a1.a1', 'center_index': 162, 'center_order': 12, 'counter': 59, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '162.20', 'image_order': 162, 'indicator': 1, 'kernel': '162.a1.a1', 'kernel_order': 12, 'label': '1944.2466.6f2', 'nt': [27, 42], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 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]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[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: 27525583
    {'center': '162.a1.a1', 'center_index': 162, 'center_order': 12, 'counter': 60, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '162.20', 'image_order': 162, 'indicator': 1, 'kernel': '162.a1.a1', 'kernel_order': 12, 'label': '1944.2466.6f3', 'nt': [27, 42], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 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]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[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: 27525584
    {'center': '162.a1.a1', 'center_index': 162, 'center_order': 12, 'counter': 61, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '486.168', 'image_order': 486, 'indicator': 0, 'kernel': '486.a1.a1', 'kernel_order': 4, 'label': '1944.2466.6g1', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[6, -3]], [[6, 3]], [[-3, 0]], [[-3, -3]], [[-3, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 3]], [[6, -3]], [[-3, 3]], [[-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, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[2, 1], [1, 2], [1, 4], [2, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [-1, -4]], [[-1, 1], [-2, 2], [-2, 4], [-1, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[2, 1], [1, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [-2, 4], [2, -4]], [[-1, 1], [-2, 2], [1, 4], [-1, -4]], [[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: 27525585
    {'center': '162.a1.a1', 'center_index': 162, 'center_order': 12, 'counter': 62, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '486.168', 'image_order': 486, 'indicator': 0, 'kernel': '486.a1.a1', 'kernel_order': 4, 'label': '1944.2466.6g2', 'nt': [54, 6], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[6, 3]], [[6, -3]], [[-3, 0]], [[-3, 3]], [[-3, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, -3]], [[6, 3]], [[-3, -3]], [[-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, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[-1, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[-1, 1], [1, 2], [-2, 4], [2, -4]], [[2, 1], [1, 2], [1, 4], [-1, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [-2, 2], [-2, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [-1, -4]], [[2, 1], [1, 2], [1, 4], [2, -4]], [[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: 27525586
    {'center': '162.a1.a1', 'center_index': 162, 'center_order': 12, 'counter': 63, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '486.168', 'image_order': 486, 'indicator': 0, 'kernel': '486.a1.a1', 'kernel_order': 4, 'label': '1944.2466.6g3', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[6, -3]], [[6, 3]], [[-3, 0]], [[-3, -3]], [[-3, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 3]], [[6, -3]], [[-3, 3]], [[-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, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [-2, 2], [-2, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[2, 1], [1, 2], [1, 4], [2, -4]], [[-1, 1], [1, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[-1, 1], [1, 2], [-2, 4], [2, -4]], [[-1, 1], [-2, 2], [1, 4], [-1, -4]], [[2, 1], [1, 2], [1, 4], [-1, -4]], [[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: 27525587
    {'center': '162.a1.a1', 'center_index': 162, 'center_order': 12, 'counter': 64, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '486.168', 'image_order': 486, 'indicator': 0, 'kernel': '486.a1.a1', 'kernel_order': 4, 'label': '1944.2466.6g4', 'nt': [54, 6], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[6, 3]], [[6, -3]], [[-3, 0]], [[-3, 3]], [[-3, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, -3]], [[6, 3]], [[-3, -3]], [[-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, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[2, 1], [1, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[-1, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [-2, 4], [2, -4]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [-1, -4]], [[2, 1], [1, 2], [1, 4], [2, -4]], [[-1, 1], [-2, 2], [-2, 4], [-1, -4]], [[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: 27525588
    {'center': '162.a1.a1', 'center_index': 162, 'center_order': 12, 'counter': 65, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '486.168', 'image_order': 486, 'indicator': 0, 'kernel': '486.a1.a1', 'kernel_order': 4, 'label': '1944.2466.6g5', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[6, -3]], [[6, 3]], [[-3, 0]], [[-3, -3]], [[-3, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 3]], [[6, -3]], [[-3, 3]], [[-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, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [-1, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [-2, 2], [-2, 4], [-1, -4]], [[2, 1], [1, 2], [1, 4], [2, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[-1, 1], [-2, 2], [1, 4], [-1, -4]], [[2, 1], [1, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [-2, 4], [2, -4]], [[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: 27525589
    {'center': '162.a1.a1', 'center_index': 162, 'center_order': 12, 'counter': 66, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '486.168', 'image_order': 486, 'indicator': 0, 'kernel': '486.a1.a1', 'kernel_order': 4, 'label': '1944.2466.6g6', 'nt': [54, 6], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[6, 3]], [[6, -3]], [[-3, 0]], [[-3, 3]], [[-3, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, -3]], [[6, 3]], [[-3, -3]], [[-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, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 2], [-2, 4], [-1, -4]], [[-1, 1], [1, 2], [-2, 4], [2, -4]], [[2, 1], [-2, 2], [1, 4], [-1, -4]], [[2, 1], [1, 2], [1, 4], [-1, -4]], [[-1, 1], [-2, 2], [1, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [2, -4]], [[2, 1], [1, 2], [1, 4], [2, -4]], [[-1, 1], [-2, 2], [-2, 4], [-1, -4]], [[-1, 1], [1, 2], [1, 4], [-1, -4]], [[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: 27525590
    {'center': '648.a1.a1', 'center_index': 648, 'center_order': 3, 'counter': 67, 'cyclotomic_n': 1, 'dim': 18, 'faithful': False, 'field': [0, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '648.278', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1.a1', 'kernel_order': 3, 'label': '1944.2466.18a', 'nt': [54, 0], 'q_character': None, 'values': [[[18, 0]], [[-6, 0]], [[0, 0]], [[18, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[3, 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]], [[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: 27525591
    {'center': '648.a1.a1', 'center_index': 648, 'center_order': 3, 'counter': 68, 'cyclotomic_n': 3, 'dim': 18, 'faithful': True, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '1944.2466', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.a1.a1', 'kernel_order': 1, 'label': '1944.2466.18b1', 'nt': [108, 0], 'q_character': None, 'values': [[[18, 0]], [[-6, 0]], [[0, 0]], [[18, -1]], [[18, 1]], [[-9, 0]], [[-9, -1]], [[-9, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 1]], [[-6, -1]], [[3, 1]], [[3, -1]], [[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]], [[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: 27525592
    {'center': '648.a1.a1', 'center_index': 648, 'center_order': 3, 'counter': 69, 'cyclotomic_n': 3, 'dim': 18, 'faithful': True, 'field': [1, -1, 1], 'group': '1944.2466', 'group_counter': 2466, 'group_order': 1944, 'image': None, 'image_isoclass': '1944.2466', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.a1.a1', 'kernel_order': 1, 'label': '1944.2466.18b2', 'nt': [108, 2], 'q_character': None, 'values': [[[18, 0]], [[-6, 0]], [[0, 0]], [[18, 1]], [[18, -1]], [[-9, 0]], [[-9, 1]], [[-9, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, -1]], [[-6, 1]], [[3, -1]], [[3, 1]], [[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]], [[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: 107441040
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 1944, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '1944.2466.1.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': '1944.2466', 'subgroup_hash': 2466, 'subgroup_order': 1944, 'subgroup_tex': 'C_9:C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441151
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 972, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2466.2.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': '972.573', 'subgroup_hash': 573, 'subgroup_order': 972, 'subgroup_tex': 'C_6^2.C_3^3', 'supersolvable': False, 'sylow': 0}
  • id: 107441219
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': True, 'centralizer_order': 3, 'characteristic': True, 'core_order': 648, 'counter': 3, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1944.2466.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.278', 'subgroup_hash': 278, 'subgroup_order': 648, 'subgroup_tex': 'C_9:C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441230
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 324, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.3.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, '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': '648.561', 'subgroup_hash': 561, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441241
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 324, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.3.c1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.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': 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': '648.467', 'subgroup_hash': 467, 'subgroup_order': 648, 'subgroup_tex': 'C_{18}.C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 107441252
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 324, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.3.d1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.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': 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': '648.560', 'subgroup_hash': 560, 'subgroup_order': 648, 'subgroup_tex': 'C_6^2:D_9', 'supersolvable': False, 'sylow': 0}
  • id: 107441263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 324, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.3.e1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.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': 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': '648.559', 'subgroup_hash': 559, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441274
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.4.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 4, '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': '486.168', 'subgroup_hash': 168, 'subgroup_order': 486, 'subgroup_tex': '(C_3^2\\times C_9):S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441285
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 324, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2466.6.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': '324.135', 'subgroup_hash': 135, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441041
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 324, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2466.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.153', 'subgroup_hash': 153, 'subgroup_order': 324, 'subgroup_tex': 'C_9:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 107441052
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 324, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2466.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.c1.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': '324.133', 'subgroup_hash': 133, 'subgroup_order': 324, 'subgroup_tex': 'C_6^2:C_9', 'supersolvable': False, 'sylow': 0}
  • id: 107441063
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 324, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2466.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.d1.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': '324.134', 'subgroup_hash': 134, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441074
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 324, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2466.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.57', 'subgroup_hash': 57, 'subgroup_order': 324, 'subgroup_tex': 'C_6^2.C_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 107441085
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 81, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.6.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': '324.140', 'subgroup_hash': 140, 'subgroup_order': 324, 'subgroup_tex': 'C_9:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 107441096
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 81, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '324.94', 'subgroup_hash': 94, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\times C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107441107
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 108, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.6.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': '324.57', 'subgroup_hash': 57, 'subgroup_order': 324, 'subgroup_tex': 'C_6^2.C_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 107441118
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 108, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.6.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': '324.57', 'subgroup_hash': 57, 'subgroup_order': 324, 'subgroup_tex': 'C_6^2.C_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 107441129
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 108, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.6.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '324.57', 'subgroup_hash': 57, 'subgroup_order': 324, 'subgroup_tex': 'C_6^2.C_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 107441140
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 108, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.6.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '324.57', 'subgroup_hash': 57, 'subgroup_order': 324, 'subgroup_tex': 'C_6^2.C_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 107441152
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 81, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '1944.2466.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 8, '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': '243.52', 'subgroup_hash': 52, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2.C_3^3', 'supersolvable': True, 'sylow': 3}
  • id: 107441163
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 108, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '216.139', 'subgroup_hash': 139, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441174
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 36, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.9.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '216.164', 'subgroup_hash': 164, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441185
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.9.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '216.57', 'subgroup_hash': 57, 'subgroup_order': 216, 'subgroup_tex': 'D_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441196
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 36, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.9.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '216.91', 'subgroup_hash': 91, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441207
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 36, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.9.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '216.91', 'subgroup_hash': 91, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441215
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 108, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.9.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '216.92', 'subgroup_hash': 92, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441216
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 108, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.9.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '216.62', 'subgroup_hash': 62, 'subgroup_order': 216, 'subgroup_tex': 'D_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441217
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 108, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.9.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '216.91', 'subgroup_hash': 91, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441218
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 108, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.9.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '216.90', 'subgroup_hash': 90, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441220
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 36, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.9.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '216.92', 'subgroup_hash': 92, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441221
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 36, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.9.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '216.92', 'subgroup_hash': 92, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441222
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.9.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '216.62', 'subgroup_hash': 62, 'subgroup_order': 216, 'subgroup_tex': 'D_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441223
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.9.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '216.62', 'subgroup_hash': 62, 'subgroup_order': 216, 'subgroup_tex': 'D_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441224
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 36, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.9.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '216.91', 'subgroup_hash': 91, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441225
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 36, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.9.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '216.91', 'subgroup_hash': 91, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441226
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 36, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.9.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '216.90', 'subgroup_hash': 90, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441227
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 36, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.9.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '216.90', 'subgroup_hash': 90, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441228
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 81, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': '162.49', 'subgroup_hash': 49, 'subgroup_order': 162, 'subgroup_tex': 'C_{18}:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107441229
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '162.34', 'subgroup_hash': 34, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441231
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 81, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '162.36', 'subgroup_hash': 36, 'subgroup_order': 162, 'subgroup_tex': 'D_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107441232
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '162.32', 'subgroup_hash': 32, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 107441233
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '162.36', 'subgroup_hash': 36, 'subgroup_order': 162, 'subgroup_tex': 'D_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107441234
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': '162.20', 'subgroup_hash': 20, 'subgroup_order': 162, 'subgroup_tex': '\\He_3.S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441235
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 108, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2466.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.45', 'subgroup_hash': 45, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 107441236
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 108, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2466.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.22', 'subgroup_hash': 22, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441237
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 108, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2466.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.31', 'subgroup_hash': 31, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441238
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 108, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2466.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.20', 'subgroup_hash': 20, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441239
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 108, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2466.18.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.21', 'subgroup_hash': 21, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441240
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.18.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': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441242
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.18.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': '108.23', 'subgroup_hash': 23, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107441243
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.18.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441244
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.18.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': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441245
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.18.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441246
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.18.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': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107441247
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.18.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '108.6', 'subgroup_hash': 6, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107441248
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.18.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '108.9', 'subgroup_hash': 9, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107441249
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.18.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '108.9', 'subgroup_hash': 9, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107441250
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.18.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '108.9', 'subgroup_hash': 9, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107441251
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 36, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.18.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': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441253
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 36, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.18.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '108.29', 'subgroup_hash': 29, 'subgroup_order': 108, 'subgroup_tex': 'C_6\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107441254
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.18.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '108.20', 'subgroup_hash': 20, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441255
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 36, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.18.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': '108.20', 'subgroup_hash': 20, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441256
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 36, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.18.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': '108.22', 'subgroup_hash': 22, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441257
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.18.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '108.31', 'subgroup_hash': 31, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441258
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.18.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '108.20', 'subgroup_hash': 20, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441259
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 36, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.18.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '108.21', 'subgroup_hash': 21, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 36, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.18.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '108.22', 'subgroup_hash': 22, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441261
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 36, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.18.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '108.22', 'subgroup_hash': 22, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.18.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.w1.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': '108.31', 'subgroup_hash': 31, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.18.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.w1.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': '108.31', 'subgroup_hash': 31, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441265
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.18.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.x1.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': '108.20', 'subgroup_hash': 20, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441266
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.18.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.x1.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': '108.20', 'subgroup_hash': 20, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441267
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 36, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.18.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.y1.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': '108.21', 'subgroup_hash': 21, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441268
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 36, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.18.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.y1.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': '108.21', 'subgroup_hash': 21, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441269
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 81, 'counter': 75, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2466.24.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': '24.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '81.13', 'subgroup_hash': 13, 'subgroup_order': 81, 'subgroup_tex': 'C_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107441270
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441271
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 27, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '81.11', 'subgroup_hash': 11, 'subgroup_order': 81, 'subgroup_tex': 'C_3^2\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107441272
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '81.13', 'subgroup_hash': 13, 'subgroup_order': 81, 'subgroup_tex': 'C_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107441273
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '81.8', 'subgroup_hash': 8, 'subgroup_order': 81, 'subgroup_tex': 'C_3.\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441275
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '81.8', 'subgroup_hash': 8, 'subgroup_order': 81, 'subgroup_tex': 'C_3.\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441276
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '81.8', 'subgroup_hash': 8, 'subgroup_order': 81, 'subgroup_tex': 'C_3.\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441277
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '81.8', 'subgroup_hash': 8, 'subgroup_order': 81, 'subgroup_tex': 'C_3.\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441278
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '81.8', 'subgroup_hash': 8, 'subgroup_order': 81, 'subgroup_tex': 'C_3.\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441279
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.27.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107441280
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.27.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 107441281
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 12, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.27.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441282
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.27.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 107441283
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.27.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 107441284
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.27.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.e1.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': 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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 107441286
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 12, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.27.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 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': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441287
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.27.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 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': '72.8', 'subgroup_hash': 8, 'subgroup_order': 72, 'subgroup_tex': 'C_9:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 107441288
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 12, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.27.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 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': '72.15', 'subgroup_hash': 15, 'subgroup_order': 72, 'subgroup_tex': 'C_2^2:D_9', 'supersolvable': False, 'sylow': 0}
  • id: 107441289
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 12, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.27.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 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': '72.15', 'subgroup_hash': 15, 'subgroup_order': 72, 'subgroup_tex': 'C_2^2:D_9', 'supersolvable': False, 'sylow': 0}
  • id: 107441290
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 27, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441291
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107441292
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107441293
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441294
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441295
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441042
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.36.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441043
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.36.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441044
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.36.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441045
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.36.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107441046
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.36.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441047
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.36.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': '54.3', 'subgroup_hash': 3, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 107441048
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.36.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': '54.3', 'subgroup_hash': 3, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 107441049
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.36.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': '54.3', 'subgroup_hash': 3, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 107441050
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.36.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441051
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.36.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': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441053
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.36.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '54.3', 'subgroup_hash': 3, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 107441054
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.36.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': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441055
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.36.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441056
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.36.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441057
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.36.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': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441058
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.36.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': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441059
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.36.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': '54.3', 'subgroup_hash': 3, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 107441060
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.36.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': '54.3', 'subgroup_hash': 3, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 107441061
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.36.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': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441062
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.36.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': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441064
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 36, 'counter': 120, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2466.54.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '54.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '54.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:S_3', 'simple': False, 'solvable': True, 'special_labels': ['S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 107441065
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 36, 'counter': 121, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2466.54.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '54.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '54.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:C_6', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 107441066
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 36, 'counter': 122, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2466.54.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '54.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '54.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 107441067
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 36, 'counter': 123, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2466.54.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '54.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '54.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 107441068
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.54.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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 107441069
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.54.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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441070
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.54.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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441071
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.54.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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441072
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.54.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441073
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.54.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107441075
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.54.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107441076
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.54.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107441077
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.54.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107441078
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.54.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107441079
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.54.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107441080
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.54.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '36.1', 'subgroup_hash': 1, 'subgroup_order': 36, 'subgroup_tex': 'C_9:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 107441081
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 12, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.54.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 107441082
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 12, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.54.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441083
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 12, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.54.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441084
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 12, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.54.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441086
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 12, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.54.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.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': 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': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107441087
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 12, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.54.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.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': 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': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107441088
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.54.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '36.3', 'subgroup_hash': 3, 'subgroup_order': 36, 'subgroup_tex': 'C_2^2:C_9', 'supersolvable': False, 'sylow': 0}
  • id: 107441089
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.54.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '36.3', 'subgroup_hash': 3, 'subgroup_order': 36, 'subgroup_tex': 'C_2^2:C_9', 'supersolvable': False, 'sylow': 0}
  • id: 107441090
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 12, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.54.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '36.3', 'subgroup_hash': 3, 'subgroup_order': 36, 'subgroup_tex': 'C_2^2:C_9', 'supersolvable': False, 'sylow': 0}
  • id: 107441091
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 12, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.54.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.w1.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': '36.3', 'subgroup_hash': 3, 'subgroup_order': 36, 'subgroup_tex': 'C_2^2:C_9', 'supersolvable': False, 'sylow': 0}
  • id: 107441092
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 4, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.54.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.x1.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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 107441093
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 4, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.54.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.y1.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': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441094
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 27, 'counter': 148, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2466.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.43', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3:S_4', '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: 107441095
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 27, 'counter': 149, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2466.72.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': '72.42', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 42, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441097
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 107441098
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.72.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': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107441099
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.72.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': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107441100
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.72.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': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107441101
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.72.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441102
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.72.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441103
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.72.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441104
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.72.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107441105
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.72.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107441106
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.72.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441108
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.72.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441109
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.72.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441110
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.72.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441111
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.72.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441112
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.72.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441113
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.72.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107441114
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.72.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 107441115
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.72.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441116
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.72.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441117
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.81.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 107441119
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 4, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.81.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.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': 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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 107441120
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 4, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.81.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.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': 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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 107441121
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 4, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.81.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.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': 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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 107441122
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.81.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.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': 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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 107441123
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 4, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.81.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.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': 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': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441124
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 9, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.108.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441125
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 3, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.108.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441126
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.108.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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441127
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.108.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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441128
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.108.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441130
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 180, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.108.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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107441131
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 181, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.108.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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107441132
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 182, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.108.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107441133
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 183, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.108.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107441134
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 184, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.108.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 107441135
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.108.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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441136
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.108.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441137
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.108.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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441138
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.108.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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441139
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.108.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441141
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.108.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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441142
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.108.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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441143
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.108.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441144
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.108.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': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 107441145
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.108.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 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': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 107441146
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.108.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 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': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 107441147
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 12, 'counter': 196, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2466.162.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '162.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '162.20', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 20, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 162, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\He_3.S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 107441148
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 12, 'counter': 197, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2466.162.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '162.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '162.41', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 41, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 162, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^3:S_3', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': False, '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: 107441149
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.162.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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441150
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.162.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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441153
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.162.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.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': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441154
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.162.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.e1.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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441155
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.162.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441156
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 203, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.162.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.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': 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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107441157
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.162.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 107441158
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 205, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.162.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.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': 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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107441159
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 206, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.162.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.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': 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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107441160
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 207, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.162.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.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': 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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107441161
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 4, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.162.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.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': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441162
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 4, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.162.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.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': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441164
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 4, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.162.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.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': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441165
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 4, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.162.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.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': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107441166
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 4, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.162.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441167
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 4, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.162.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 107441168
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': True, 'core_order': 9, 'counter': 214, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2466.216.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.95', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 95, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2:S_4', 'simple': False, 'solvable': True, 'special_labels': [], '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: 107441169
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 9, 'counter': 215, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2466.216.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.164', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 164, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2:S_4', '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: 107441170
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 9, 'counter': 216, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2466.216.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.95', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 95, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2:S_4', 'simple': False, 'solvable': True, 'special_labels': [], '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: 107441171
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 9, 'counter': 217, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2466.216.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.95', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 95, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2:S_4', 'simple': False, 'solvable': True, 'special_labels': [], '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: 107441172
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 3, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.216.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 107441173
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.216.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 107441175
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.216.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, '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: 107441176
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.216.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, '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: 107441177
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 222, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.216.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, '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: 107441178
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 223, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.216.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, '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: 107441179
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 224, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.216.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, '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: 107441180
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 225, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.216.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, '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: 107441181
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 226, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.216.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, '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: 107441182
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 227, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.216.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, '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: 107441183
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.216.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, '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: 107441184
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.216.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, '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: 107441186
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 4, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1944.2466.243.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '243.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': 243, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 2}
  • id: 107441187
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 3, 'counter': 231, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.324.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, '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: 107441188
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 232, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.324.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 107441189
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 233, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.324.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 107441190
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 234, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.324.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 107441191
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 235, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.324.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, '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: 107441192
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 236, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.324.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.e1.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': 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: 107441193
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 237, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.324.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, '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: 107441194
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 238, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.324.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, '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: 107441195
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 239, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.324.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, '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: 107441197
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 240, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.324.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, '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: 107441198
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.324.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.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': 324, '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: 107441199
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.324.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.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': 324, '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: 107441200
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 4, 'counter': 243, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.2466.486.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '486.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '486.168', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 168, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 486, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '(C_3^2\\times C_9):S_3', 'simple': False, 'solvable': True, 'special_labels': ['C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 107441201
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.2466.486.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.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': 486, '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: 107441202
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 245, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.486.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.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': 486, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 107441203
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': True, 'central_factor': False, 'centralizer_order': 1944, 'characteristic': True, 'core_order': 3, 'counter': 246, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '1944.2466.648.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '648.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '648.278', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 278, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_9:C_3:S_4', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107441204
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': True, 'core_order': 3, 'counter': 247, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1944.2466.648.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '648.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '648.572', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 572, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^3:S_4', '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: 107441205
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': False, 'core_order': 1, 'counter': 248, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.648.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, '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: 107441206
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 1, 'counter': 249, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.648.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, '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: 107441208
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 1, 'counter': 250, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.648.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, '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: 107441209
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 1, 'counter': 251, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.648.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.e1.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': 648, '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: 107441210
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 252, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.648.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, '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: 107441211
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 253, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.648.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, '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: 107441212
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 1, 'counter': 254, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.972.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.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': 972, '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: 107441213
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 255, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.2466.972.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.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': 972, '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: 107441214
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.2466', 'ambient_counter': 2466, 'ambient_order': 1944, 'ambient_tex': 'C_9:C_3^2:S_4', 'central': True, 'central_factor': False, 'centralizer_order': 1944, 'characteristic': True, 'core_order': 1, 'counter': 256, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1944.2466.1944.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1944.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '1944.2466', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2466, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1944, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_9:C_3^2:S_4', '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: 107441040
    {'ambient': '1944.2466', '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': '648.a1.a1', 'complements': ['1944.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '3.a1.a1', '3.b1.a1', '3.c1.a1', '3.d1.a1', '3.e1.a1', '4.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6280, 5935, 4014, 3984, 3322, 5551, 7032, 2307], 'generators': [3, 1332, 648, 2, 936, 972, 54, 6], 'label': '1944.2466.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '648.278', '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': '648.278'}
  • id: 107441041
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '108.28', 'aut_weyl_index': 36, 'centralizer': '54.a1.a1', 'complements': ['324.j1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.c1.a1'], 'contains': ['12.a1.a1', '18.a1.a1', '18.c1.a1', '18.o1.a1', '18.s1.a1', '18.w1.a1', '18.w1.b1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5381, 8648, 6042, 1307, 5125, 8203, 5140, 7998], 'generators': [54, 648, 1332, 972, 2, 936], 'label': '1944.2466.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['18.a1.a1', '18.c1.a1', '24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '648.278', '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': '54.8'}
  • id: 107441042
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '18.3', 'aut_weyl_index': 216, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.i1.b1', '18.m1.b1', '18.w1.b1'], 'contains': ['72.o1.b1', '108.d1.b1', '108.e1.a1', '108.h1.a1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [3435, -1, 9358, -1, 5951, -1, 4417, -1], 'generators': [54, 1334, 936, 648], 'label': '1944.2466.36.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.f1.b1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 107441043
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '9.2', 'aut_weyl_index': 432, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.w1.a1'], 'contains': ['72.o1.a1', '108.d1.a1', '108.f1.a1', '108.g1.a1', '108.h1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4118, -1, 8455, -1, 4932, -1, 5150, -1], 'generators': [972, 722, 936, 648], 'label': '1944.2466.36.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '36.g1.a1', 'projective_image': '1944.2466', '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': '9.2'}
  • id: 107441044
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '9.2', 'aut_weyl_index': 432, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.w1.b1'], 'contains': ['72.o1.b1', '108.d1.b1', '108.f1.a1', '108.g1.a1', '108.h1.b1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [4118, -1, 9082, -1, 4932, -1, 5666, -1], 'generators': [972, 1334, 936, 648], 'label': '1944.2466.36.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '36.g1.b1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.b1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 107441045
    {'ambient': '1944.2466', 'aut_centralizer_order': 18, 'aut_label': '36.h1', '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.b1.a1', '12.c1.a1', '12.d1.a1', '12.e1.a1', '18.f1.a1'], 'contains': ['72.a1.a1', '108.j1.a1', '108.k1.a1', '108.m1.a1', '108.n1.a1', '108.n1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5895, -1, 5923, -1, 3103, -1, 6551, -1], 'generators': [3, 2, 1332, 648], 'label': '1944.2466.36.h1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '36.h1.a1', 'projective_image': '648.278', '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': '6.1'}
  • id: 107441046
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '108.25', 'aut_weyl_index': 36, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1.a1', '12.b1.a1'], 'contains': ['72.c1.a1', '108.k1.a1', '108.l1.a1', '108.o1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2154, -1, 2610, -1, 5745, -1, 2110, -1], 'generators': [3, 2, 6, 648], 'label': '1944.2466.36.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '36.i1.a1', 'projective_image': '648.278', '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': '54.5'}
  • id: 107441047
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '108.26', 'aut_weyl_index': 36, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '18.g1.a1'], 'contains': ['72.d1.a1', '108.k1.a1', '108.p1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4954, -1, 9782, -1, 4213, -1, 6098, -1], 'generators': [3, 2, 936, 648], 'label': '1944.2466.36.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '36.j1.a1', 'projective_image': '648.278', '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': '54.6'}
  • id: 107441048
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '108.26', 'aut_weyl_index': 36, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.d1.a1', '12.d1.a1'], 'contains': ['72.e1.a1', '108.k1.a1', '108.q1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6898, -1, 4255, -1, 3409, -1, 9651, -1], 'generators': [3, 2, 1806, 648], 'label': '1944.2466.36.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '36.k1.a1', 'projective_image': '648.278', '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': '18.1'}
  • id: 107441049
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '108.26', 'aut_weyl_index': 36, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.e1.a1', '12.e1.a1'], 'contains': ['72.f1.a1', '108.k1.a1', '108.r1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9345, -1, 4672, -1, 73, -1, 7622, -1], 'generators': [3, 2, 906, 648], 'label': '1944.2466.36.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '36.l1.a1', 'projective_image': '648.278', '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': '54.6'}
  • id: 107441050
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '54.5', 'aut_weyl_index': 72, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.f1.a1', '12.b1.a1', '12.f1.a1'], 'contains': ['72.g1.a1', '108.m1.a1', '108.o1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5623, -1, 5768, -1, 3262, -1, 6686, -1], 'generators': [3, 1332, 6, 648], 'label': '1944.2466.36.m1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '36.m1.a1', 'projective_image': '1944.2466', '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': '54.5'}
  • id: 107441051
    {'ambient': '1944.2466', 'aut_centralizer_order': 12, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '54.6', 'aut_weyl_index': 72, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.f1.a1', '18.h1.a1'], 'contains': ['72.b1.a1', '108.m1.a1', '108.p1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6288, -1, 9237, -1, 2496, -1, 7087, -1], 'generators': [3, 1332, 936, 648], 'label': '1944.2466.36.n1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '36.n1.a1', 'projective_image': '1944.2466', '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': '54.6'}
  • id: 107441052
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '6.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '432.761', 'aut_weyl_index': 9, 'centralizer': '72.a1.a1', 'complements': ['324.j1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.d1.a1'], 'contains': ['18.a1.a1', '18.d1.a1', '18.p1.a1', '18.t1.a1', '18.x1.a1', '18.x1.b1', '24.c1.a1'], 'core': '6.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6437, 2998, 2723, 8849, 3451, 4720, 8541, 5844], 'generators': [2, 972, 54, 1122, 1332, 648], 'label': '1944.2466.6.c1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.c1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['18.a1.a1', '18.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '648.278', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 107441053
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '54.6', 'aut_weyl_index': 72, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.h1.a1', '12.d1.a1', '12.f1.a1'], 'contains': ['72.j1.a1', '108.m1.a1', '108.q1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7179, -1, 6095, -1, 2101, -1, 9427, -1], 'generators': [3, 1332, 1806, 648], 'label': '1944.2466.36.o1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '36.o1.a1', 'projective_image': '1944.2466', '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': '18.1'}
  • id: 107441054
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '54.6', 'aut_weyl_index': 72, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.i1.a1', '12.e1.a1', '12.f1.a1'], 'contains': ['72.l1.a1', '108.m1.a1', '108.r1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9089, -1, 6485, -1, 814, -1, 7958, -1], 'generators': [3, 1332, 906, 648], 'label': '1944.2466.36.p1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '36.p1.a1', 'projective_image': '1944.2466', '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': '54.6'}
  • id: 107441055
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '54.5', 'aut_weyl_index': 72, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.j1.a1', '12.b1.a1'], 'contains': ['72.n1.a1', '108.n1.a1', '108.o1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2776, -1, 2828, -1, 4360, -1, 4558, -1], 'generators': [3, 722, 6, 648], 'label': '1944.2466.36.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '36.q1.a1', 'projective_image': '1944.2466', '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': '54.5'}
  • id: 107441056
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '54.5', 'aut_weyl_index': 72, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.j1.b1', '12.b1.a1'], 'contains': ['72.n1.b1', '108.n1.b1', '108.o1.a1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [2776, -1, 2734, -1, 4360, -1, 4663, -1], 'generators': [3, 1334, 6, 648], 'label': '1944.2466.36.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '36.q1.b1', 'projective_image': '1944.2466', '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': '54.5'}
  • id: 107441057
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '54.6', 'aut_weyl_index': 72, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '18.i1.a1'], 'contains': ['72.o1.a1', '108.n1.a1', '108.p1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4445, -1, 9890, -1, 4072, -1, 5977, -1], 'generators': [3, 722, 936, 648], 'label': '1944.2466.36.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '36.r1.a1', 'projective_image': '1944.2466', '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': '54.6'}
  • id: 107441058
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '54.6', 'aut_weyl_index': 72, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '18.i1.b1'], 'contains': ['72.o1.b1', '108.n1.b1', '108.p1.a1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [4445, -1, 9975, -1, 4072, -1, 6218, -1], 'generators': [3, 1334, 936, 648], 'label': '1944.2466.36.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '36.r1.b1', 'projective_image': '1944.2466', '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': '54.6'}
  • id: 107441059
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '54.6', 'aut_weyl_index': 72, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.l1.a1', '12.d1.a1'], 'contains': ['72.p1.a1', '108.n1.a1', '108.q1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5491, -1, 4128, -1, 2684, -1, 9794, -1], 'generators': [3, 722, 1806, 648], 'label': '1944.2466.36.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '36.s1.a1', 'projective_image': '1944.2466', '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': '18.1'}
  • id: 107441060
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '54.6', 'aut_weyl_index': 72, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.l1.b1', '12.d1.a1'], 'contains': ['72.p1.b1', '108.n1.b1', '108.q1.a1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [5491, -1, 4001, -1, 2684, -1, 9937, -1], 'generators': [3, 1334, 1806, 648], 'label': '1944.2466.36.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '36.s1.b1', 'projective_image': '1944.2466', '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': '18.1'}
  • id: 107441061
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '54.6', 'aut_weyl_index': 72, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.m1.a1', '12.e1.a1'], 'contains': ['72.q1.a1', '108.n1.a1', '108.r1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9600, -1, 5607, -1, 309, -1, 7501, -1], 'generators': [3, 722, 906, 648], 'label': '1944.2466.36.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '36.t1.a1', 'projective_image': '1944.2466', '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': '54.6'}
  • id: 107441062
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '54.6', 'aut_weyl_index': 72, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.m1.b1', '12.e1.a1'], 'contains': ['72.q1.b1', '108.n1.b1', '108.r1.a1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [9600, -1, 5521, -1, 309, -1, 7822, -1], 'generators': [3, 1334, 906, 648], 'label': '1944.2466.36.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '36.t1.b1', 'projective_image': '1944.2466', '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': '54.6'}
  • id: 107441063
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '6.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '432.538', 'aut_weyl_index': 9, 'centralizer': '216.a1.a1', 'complements': ['324.j1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.e1.a1'], 'contains': ['18.a1.a1', '18.e1.a1', '18.q1.a1', '18.u1.a1', '18.y1.a1', '18.y1.b1', '24.d1.a1'], 'core': '6.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9279, 5090, 3934, 4817, 1308, 846, 6948, 2155], 'generators': [2, 972, 54, 942, 1332, 648], 'label': '1944.2466.6.d1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.d1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['18.a1.a1', '18.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '648.278', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '216.95'}
  • id: 107441064
    {'ambient': '1944.2466', 'aut_centralizer_order': 324, 'aut_label': '54.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.n1.a1', '18.o1.a1', '18.p1.a1', '18.q1.a1', '27.b1.a1'], 'contains': ['108.a1.a1', '162.a1.a1', '162.b1.a1', '162.k1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5323, 2312, 1790, 8308, 7311, 2578, 2945, 8399], 'generators': [54, 972, 2, 648], 'label': '1944.2466.54.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': ['18.a1.a1'], 'normal_contains': ['162.a1.a1', '162.b1.a1', '216.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '54.a1.a1', 'projective_image': '648.278', 'quotient_action_image': '6.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '54.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107441065
    {'ambient': '1944.2466', 'aut_centralizer_order': 216, 'aut_label': '54.b1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '18.4', 'aut_weyl_index': 216, 'centralizer': '18.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.b1.a1', '18.c1.a1', '18.d1.a1', '18.e1.a1', '18.r1.a1', '18.s1.a1', '18.t1.a1', '18.u1.a1', '27.d1.a1'], 'contains': ['108.c1.a1', '162.b1.a1', '162.l1.a1'], 'core': '54.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7926, 4963, 5036, 4380, 3730, 4219, 6996, 4357], 'generators': [54, 972, 1332, 648], 'label': '1944.2466.54.b1.a1', 'mobius_quo': 0, 'mobius_sub': 27, 'normal_closure': '54.b1.a1', 'normal_contained_in': ['18.a1.a1', '18.b1.a1', '18.c1.a1', '18.d1.a1', '18.e1.a1'], 'normal_contains': ['162.b1.a1', '216.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '54.b1.a1', 'projective_image': '1944.2466', 'quotient_action_image': '18.4', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '54.b1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107441066
    {'ambient': '1944.2466', 'aut_centralizer_order': 108, 'aut_label': '54.c1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '18.4', 'aut_weyl_index': 216, 'centralizer': '18.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.v1.a1', '18.w1.a1', '18.x1.a1', '18.y1.a1', '27.e1.a1'], 'contains': ['108.d1.a1', '162.b1.a1', '162.m1.a1'], 'core': '54.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4878, 3242, 2411, 6589, 6415, 3398, 3762, 7617], 'generators': [54, 972, 722, 648], 'label': '1944.2466.54.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '54.c1.a1', 'normal_contained_in': ['18.a1.a1'], 'normal_contains': ['162.b1.a1', '216.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '54.c1.a1', 'projective_image': '1944.2466', 'quotient_action_image': '18.4', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '54.c1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107441067
    {'ambient': '1944.2466', 'aut_centralizer_order': 108, 'aut_label': '54.c1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '18.4', 'aut_weyl_index': 216, 'centralizer': '18.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.v1.b1', '18.w1.b1', '18.x1.b1', '18.y1.b1', '27.e1.b1'], 'contains': ['108.d1.b1', '162.b1.a1', '162.m1.b1'], 'core': '54.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4878, 3242, 1956, 7443, 6415, 3398, 3847, 6054], 'generators': [54, 972, 1334, 648], 'label': '1944.2466.54.c1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '54.c1.b1', 'normal_contained_in': ['18.a1.a1'], 'normal_contains': ['162.b1.a1', '216.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '54.c1.b1', 'projective_image': '1944.2466', 'quotient_action_image': '18.4', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '54.c1.b1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107441068
    {'ambient': '1944.2466', '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.f1.a1', '27.a1.a1'], 'contains': ['108.b1.a1', '108.j1.a1', '162.c1.a1', '162.d1.a1', '162.e1.a1', '162.e1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1069, -1, 2300, -1, 7210, -1, 2859, -1], 'generators': [3, 54, 2, 36], 'label': '1944.2466.54.d1.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': '54.d1.a1', 'projective_image': '648.278', '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: 107441069
    {'ambient': '1944.2466', 'aut_centralizer_order': 18, 'aut_label': '54.e1', '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': ['18.f1.a1', '18.g1.a1', '27.b1.a1'], 'contains': ['108.a1.a1', '108.k1.a1', '162.c1.a1', '162.f1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1909, -1, 4384, -1, 7076, -1, 3059, -1], 'generators': [3, 54, 2, 648], 'label': '1944.2466.54.e1.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': '54.e1.a1', 'projective_image': '648.278', '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': '12.4'}
  • id: 107441070
    {'ambient': '1944.2466', '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': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1.a1', '18.h1.a1', '27.d1.a1'], 'contains': ['108.c1.a1', '108.m1.a1', '162.d1.a1', '162.f1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3396, -1, 5545, -1, 6550, -1, 3647, -1], 'generators': [3, 54, 1332, 648], 'label': '1944.2466.54.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.f1.a1', 'projective_image': '1944.2466', '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': '12.4'}
  • id: 107441071
    {'ambient': '1944.2466', '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.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1.a1', '18.i1.a1', '27.e1.a1'], 'contains': ['108.d1.a1', '108.n1.a1', '162.e1.a1', '162.f1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1417, -1, 5420, -1, 6716, -1, 3200, -1], 'generators': [3, 54, 722, 648], 'label': '1944.2466.54.g1.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': '54.g1.a1', 'projective_image': '1944.2466', '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': '12.4'}
  • id: 107441072
    {'ambient': '1944.2466', '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.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1.a1', '18.i1.b1', '27.e1.b1'], 'contains': ['108.d1.b1', '108.n1.b1', '162.e1.b1', '162.f1.a1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [1417, -1, 4687, -1, 6716, -1, 3506, -1], 'generators': [3, 54, 1334, 648], 'label': '1944.2466.54.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.g1.b1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.g1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107441073
    {'ambient': '1944.2466', 'aut_centralizer_order': 12, 'aut_label': '54.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '108.26', 'aut_weyl_index': 36, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1.a1', '18.h1.a1', '18.i1.a1', '18.i1.b1', '27.g1.a1'], 'contains': ['108.e1.a1', '108.p1.a1', '162.f1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3185, -1, 9435, -1, 6309, -1, 3938, -1], 'generators': [3, 54, 936, 648], 'label': '1944.2466.54.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '54.h1.a1', 'projective_image': '1944.2466', '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': '108.26'}
  • id: 107441074
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '6.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '648.572', 'aut_weyl_index': 6, 'centralizer': '216.a1.a1', 'complements': ['324.f1.a1', '324.h1.b1', '324.h1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['18.b1.a1', '18.c1.a1', '18.d1.a1', '18.e1.a1', '24.e1.a1'], 'core': '6.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7176, 6727, 4252, 3203, 3199, 6381, 7278, 677], 'generators': [6, 972, 54, 936, 1332, 648], 'label': '1944.2466.6.e1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.e1.a1', 'normal_contained_in': ['2.a1.a1', '3.a1.a1'], 'normal_contains': ['18.b1.a1', '18.c1.a1', '18.d1.a1', '18.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '1944.2466', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '216.95'}
  • id: 107441075
    {'ambient': '1944.2466', 'aut_centralizer_order': 18, 'aut_label': '54.i1', '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': ['18.j1.a1', '18.k1.a1', '27.b1.a1'], 'contains': ['108.a1.a1', '162.g1.a1', '162.h1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1249, -1, 3319, -1, 8350, -1, 1441, -1], 'generators': [975, 2, 54, 648], 'label': '1944.2466.54.i1.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': '54.i1.a1', 'projective_image': '648.278', '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': '12.4'}
  • id: 107441076
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '54.j1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 972, 'centralizer': '54.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.j1.a1', '27.a1.a1'], 'contains': ['108.b1.a1', '162.g1.a1', '162.i1.a1', '162.j1.a1', '162.j1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [358, -1, 1178, -1, 8891, -1, 838, -1], 'generators': [975, 2, 36, 54], 'label': '1944.2466.54.j1.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': '54.j1.a1', 'projective_image': '648.278', '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': '2.1'}
  • id: 107441077
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '54.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.j1.a1', '18.l1.a1', '27.d1.a1'], 'contains': ['108.c1.a1', '162.h1.a1', '162.i1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2787, -1, 3665, -1, 7838, -1, 2461, -1], 'generators': [975, 1332, 54, 648], 'label': '1944.2466.54.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.k1.a1', 'projective_image': '1944.2466', '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': '12.4'}
  • id: 107441078
    {'ambient': '1944.2466', 'aut_centralizer_order': 18, 'aut_label': '54.l1', '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': ['18.j1.a1', '18.m1.a1', '27.e1.a1'], 'contains': ['108.d1.a1', '162.h1.a1', '162.j1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [735, -1, 3890, -1, 8044, -1, 1616, -1], 'generators': [975, 722, 54, 648], 'label': '1944.2466.54.l1.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': '54.l1.a1', 'projective_image': '1944.2466', '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': '12.4'}
  • id: 107441079
    {'ambient': '1944.2466', 'aut_centralizer_order': 18, 'aut_label': '54.l1', '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': ['18.j1.a1', '18.m1.b1', '27.e1.b1'], 'contains': ['108.d1.b1', '162.h1.a1', '162.j1.b1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [735, -1, 3510, -1, 8044, -1, 1935, -1], 'generators': [975, 1334, 54, 648], 'label': '1944.2466.54.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.l1.b1', 'projective_image': '1944.2466', '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': '12.4'}
  • id: 107441080
    {'ambient': '1944.2466', 'aut_centralizer_order': 12, 'aut_label': '54.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '108.26', 'aut_weyl_index': 36, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.k1.a1', '18.l1.a1', '18.m1.a1', '18.m1.b1', '27.g1.a1'], 'contains': ['108.e1.a1', '162.h1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1781, -1, 8749, -1, 7633, -1, 2324, -1], 'generators': [975, 54, 936, 648], 'label': '1944.2466.54.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '54.m1.a1', 'projective_image': '1944.2466', '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': '108.26'}
  • id: 107441081
    {'ambient': '1944.2466', 'aut_centralizer_order': 108, 'aut_label': '54.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '27.a1.a1'], 'contains': ['108.b1.a1', '162.a1.a1', '162.l1.a1', '162.m1.a1', '162.m1.b1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2116, -1, 957, -1, 8197, -1, 2590, -1], 'generators': [54, 972, 2, 1332], 'label': '1944.2466.54.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '54.n1.a1', 'projective_image': '648.278', '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: 107441082
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '54.o1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.48', 'aut_weyl_index': 81, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.n1.a1', '27.c1.a1'], 'contains': ['162.a1.a1', '162.n1.a1', '162.o1.a1', '216.e1.a1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [525, -1, 106, -1, 9839, -1, 137, -1], 'generators': [2, 6, 54, 972], 'label': '1944.2466.54.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '54.o1.a1', 'projective_image': '648.278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.o1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107441083
    {'ambient': '1944.2466', 'aut_centralizer_order': 18, 'aut_label': '54.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.42', 'aut_weyl_index': 54, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '18.n1.a1', '18.v1.a1', '18.v1.b1', '27.f1.a1'], 'contains': ['162.b1.a1', '162.n1.a1', '216.f1.a1'], 'core': '162.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1612, -1, 500, -1, 9457, -1, 541, -1], 'generators': [6, 648, 54, 972], 'label': '1944.2466.54.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '54.p1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.p1.a1', 'subgroup_fusion': None, 'weyl_group': '72.42'}
  • id: 107441084
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '54.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.42', 'aut_weyl_index': 54, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.n1.a1', '18.r1.a1', '18.v1.a1', '18.v1.b1'], 'contains': ['162.b1.a1', '162.o1.a1', '216.g1.a1'], 'core': '162.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2237, -1, 626, -1, 9243, -1, 682, -1], 'generators': [8, 648, 54, 972], 'label': '1944.2466.54.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '54.q1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.q1.a1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 107441085
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '216.111', 'aut_weyl_index': 18, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.a1'], 'contains': ['12.a1.a1', '12.c1.a1', '18.f1.a1', '18.g1.a1', '18.h1.a1', '18.i1.a1', '18.i1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3247, -1, 9043, -1, 5393, -1, 4405, -1], 'generators': [3, 648, 936, 54, 2, 1332], 'label': '1944.2466.6.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '6.f1.a1', 'projective_image': '648.278', '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': '108.26'}
  • id: 107441086
    {'ambient': '1944.2466', 'aut_centralizer_order': 216, 'aut_label': '54.r1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.2', 'aut_weyl_index': 648, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '18.o1.a1', '18.w1.a1', '18.w1.b1', '27.g1.a1'], 'contains': ['108.e1.a1', '108.f1.a1', '162.b1.a1'], 'core': '162.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4699, -1, 8312, -1, 5336, -1, 4802, -1], 'generators': [54, 972, 936, 648], 'label': '1944.2466.54.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '54.r1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.r1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 107441087
    {'ambient': '1944.2466', 'aut_centralizer_order': 108, 'aut_label': '54.s1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 648, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.o1.a1', '18.s1.a1', '18.w1.a1', '18.w1.b1'], 'contains': ['108.g1.a1', '108.h1.a1', '108.h1.b1', '162.b1.a1'], 'core': '162.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5143, -1, 7699, -1, 4523, -1, 5322, -1], 'generators': [54, 972, 938, 648], 'label': '1944.2466.54.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '54.s1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.s1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 107441088
    {'ambient': '1944.2466', 'aut_centralizer_order': 18, 'aut_label': '54.t1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.42', 'aut_weyl_index': 54, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '18.p1.a1', '18.x1.a1', '18.x1.b1', '27.h1.a1'], 'contains': ['162.b1.a1', '216.j1.a1'], 'core': '162.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6330, -1, 1667, -1, 3898, -1, 9296, -1], 'generators': [1122, 648, 54, 972], 'label': '1944.2466.54.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '54.t1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.t1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107441089
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '54.u1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.42', 'aut_weyl_index': 54, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.p1.a1', '18.t1.a1', '18.x1.a1', '18.x1.b1'], 'contains': ['162.b1.a1', '216.k1.a1'], 'core': '162.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6978, -1, 1519, -1, 3563, -1, 9136, -1], 'generators': [950, 648, 54, 972], 'label': '1944.2466.54.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '54.u1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.u1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 107441090
    {'ambient': '1944.2466', 'aut_centralizer_order': 18, 'aut_label': '54.v1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.42', 'aut_weyl_index': 54, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1.a1', '18.q1.a1', '18.y1.a1', '18.y1.b1', '27.i1.a1'], 'contains': ['162.b1.a1', '216.l1.a1'], 'core': '162.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9851, -1, 3085, -1, 687, -1, 7275, -1], 'generators': [942, 648, 54, 972], 'label': '1944.2466.54.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.e1.a1', 'old_label': '54.v1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.v1.a1', 'subgroup_fusion': None, 'weyl_group': '72.42'}
  • id: 107441091
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '54.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.42', 'aut_weyl_index': 54, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.q1.a1', '18.u1.a1', '18.y1.a1', '18.y1.b1'], 'contains': ['162.b1.a1', '216.m1.a1'], 'core': '162.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9716, -1, 3190, -1, 941, -1, 7393, -1], 'generators': [944, 648, 54, 972], 'label': '1944.2466.54.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '54.w1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.w1.a1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 107441092
    {'ambient': '1944.2466', 'aut_centralizer_order': 108, 'aut_label': '54.x1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1'], 'contains': ['108.i1.a1', '162.k1.a1', '162.l1.a1', '162.m1.a1', '162.m1.b1'], 'core': '486.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5542, -1, 2209, -1, 7412, -1, 2773, -1], 'generators': [54, 972, 650, 1332], 'label': '1944.2466.54.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '54.x1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.x1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 107441093
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '54.y1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.12', 'aut_weyl_index': 162, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.n1.a1'], 'contains': ['162.k1.a1', '162.n1.a1', '162.o1.a1', '216.o1.a1'], 'core': '486.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [947, -1, 268, -1, 9672, -1, 279, -1], 'generators': [650, 6, 54, 972], 'label': '1944.2466.54.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1.a1', 'old_label': '54.y1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.y1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 107441094
    {'ambient': '1944.2466', 'aut_centralizer_order': 324, 'aut_label': '72.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '6.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.b1.a1', '24.c1.a1', '24.d1.a1', '36.a1.a1', '36.h1.a1'], 'contains': ['216.a1.a1', '216.b1.a1', '216.c1.a1', '216.c1.b1', '216.d1.a1', '216.n1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6553, 5766, 6301, 4755, 2969, 5180, 6366, 6835], 'generators': [2, 1332, 648], 'label': '1944.2466.72.a1.a1', 'mobius_quo': 0, 'mobius_sub': 108, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['18.a1.a1', '24.a1.a1'], 'normal_contains': ['216.a1.a1', '216.c1.b1', '216.c1.a1', '216.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '648.278', 'quotient_action_image': '6.1', 'quotient_action_kernel': '12.3', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107441095
    {'ambient': '1944.2466', 'aut_centralizer_order': 72, 'aut_label': '72.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '54.8', 'aut_weyl_index': 72, 'centralizer': '54.a1.a1', 'complements': ['27.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.e1.a1', '24.g1.a1', '36.d1.a1', '36.n1.a1'], 'contains': ['216.b1.a1', '216.h1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6989, 8026, 8526, 1838, 2416, 7472, 7087, 5186], 'generators': [936, 1332], 'label': '1944.2466.72.b1.a1', 'mobius_quo': 0, 'mobius_sub': 12, 'normal_closure': '72.b1.a1', 'normal_contained_in': ['18.c1.a1', '24.a1.a1'], 'normal_contains': ['216.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.b1.a1', 'projective_image': '1944.2466', 'quotient_action_image': '6.1', 'quotient_action_kernel': '12.5', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '54.8'}
  • id: 107441096
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '216.111', 'aut_weyl_index': 18, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.a1'], 'contains': ['12.a1.a1', '18.j1.a1', '18.k1.a1', '18.l1.a1', '18.m1.a1', '18.m1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2154, -1, 7778, -1, 7055, -1, 2996, -1], 'generators': [975, 648, 936, 2, 1332, 54], 'label': '1944.2466.6.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '6.g1.a1', 'projective_image': '648.278', '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': '108.26'}
  • id: 107441097
    {'ambient': '1944.2466', 'aut_centralizer_order': 27, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.5', 'aut_weyl_index': 324, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.n1.a1', '24.b1.a1', '36.i1.a1'], 'contains': ['216.a1.a1', '216.e1.a1', '216.f1.a1', '216.g1.a1', '216.o1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2116, -1, 2746, -1, 5760, -1, 2817, -1], 'generators': [2, 6, 648], 'label': '1944.2466.72.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '72.c1.a1', 'projective_image': '648.278', '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': '6.2'}
  • id: 107441098
    {'ambient': '1944.2466', 'aut_centralizer_order': 108, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.5', 'aut_weyl_index': 324, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.b1.a1', '36.c1.a1', '36.j1.a1'], 'contains': ['216.a1.a1', '216.h1.a1', '216.i1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4887, -1, 9056, -1, 4586, -1, 5650, -1], 'generators': [2, 936], 'label': '1944.2466.72.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '72.d1.a1', 'projective_image': '648.278', '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': '6.2'}
  • id: 107441099
    {'ambient': '1944.2466', 'aut_centralizer_order': 27, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.5', 'aut_weyl_index': 324, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.p1.a1', '24.c1.a1', '36.k1.a1'], 'contains': ['216.a1.a1', '216.j1.a1', '216.k1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7140, -1, 4203, -1, 3409, -1, 8937, -1], 'generators': [2, 1122], 'label': '1944.2466.72.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '72.e1.a1', 'projective_image': '648.278', '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: 107441100
    {'ambient': '1944.2466', 'aut_centralizer_order': 27, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.5', 'aut_weyl_index': 324, 'centralizer': '72.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.q1.a1', '24.d1.a1', '36.l1.a1'], 'contains': ['216.a1.a1', '216.l1.a1', '216.m1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9404, -1, 4838, -1, 445, -1, 7617, -1], 'generators': [2, 942], 'label': '1944.2466.72.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '72.f1.a1', 'projective_image': '648.278', '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': '6.2'}
  • id: 107441101
    {'ambient': '1944.2466', 'aut_centralizer_order': 18, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '54.8', 'aut_weyl_index': 72, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '24.b1.a1', '24.e1.a1', '24.f1.a1', '36.m1.a1'], 'contains': ['216.b1.a1', '216.f1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7362, -1, 6229, -1, 3231, -1, 6933, -1], 'generators': [6, 1332], 'label': '1944.2466.72.g1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '72.g1.a1', 'projective_image': '1944.2466', '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': '54.8'}
  • id: 107441102
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '54.8', 'aut_weyl_index': 72, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.r1.a1', '24.b1.a1', '24.g1.a1', '24.h1.a1', '24.i1.a1'], 'contains': ['216.b1.a1', '216.g1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8568, -1, 6864, -1, 1855, -1, 8348, -1], 'generators': [8, 1332], 'label': '1944.2466.72.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.h1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1.a1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 107441103
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '54.8', 'aut_weyl_index': 72, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.f1.a1', '24.h1.a1', '24.i1.a1', '36.e1.a1'], 'contains': ['216.b1.a1', '216.i1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8095, -1, 7324, -1, 1986, -1, 7832, -1], 'generators': [938, 1332], 'label': '1944.2466.72.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.i1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1.a1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 107441104
    {'ambient': '1944.2466', 'aut_centralizer_order': 54, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '18.3', 'aut_weyl_index': 216, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '24.c1.a1', '24.e1.a1', '24.h1.a1', '36.o1.a1'], 'contains': ['216.b1.a1', '216.j1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7478, -1, 6616, -1, 2126, -1, 8794, -1], 'generators': [1122, 1332], 'label': '1944.2466.72.j1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '72.j1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107441105
    {'ambient': '1944.2466', 'aut_centralizer_order': 27, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '18.3', 'aut_weyl_index': 216, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.t1.a1', '24.c1.a1', '24.f1.a1', '24.g1.a1', '24.i1.a1'], 'contains': ['216.b1.a1', '216.k1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7967, -1, 7040, -1, 1727, -1, 8633, -1], 'generators': [950, 1332], 'label': '1944.2466.72.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.k1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.k1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 107441106
    {'ambient': '1944.2466', 'aut_centralizer_order': 18, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '54.8', 'aut_weyl_index': 72, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1.a1', '24.d1.a1', '24.e1.a1', '24.i1.a1', '36.p1.a1'], 'contains': ['216.b1.a1', '216.l1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9150, -1, 6722, -1, 1034, -1, 7958, -1], 'generators': [942, 1332], 'label': '1944.2466.72.l1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '72.l1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.l1.a1', 'subgroup_fusion': None, 'weyl_group': '54.8'}
  • id: 107441107
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '648.572', 'aut_weyl_index': 6, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['18.b1.a1', '18.s1.a1', '18.t1.a1', '18.u1.a1', '24.f1.a1'], 'core': '18.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8230, -1, 5012, -1, 2787, -1, 7110, -1], 'generators': [938, 972, 54, 6, 1332, 648], 'label': '1944.2466.6.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '6.h1.a1', 'projective_image': '1944.2466', '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': '108.22'}
  • id: 107441108
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '72.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '54.8', 'aut_weyl_index': 72, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.u1.a1', '24.d1.a1', '24.f1.a1', '24.g1.a1', '24.h1.a1'], 'contains': ['216.b1.a1', '216.m1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8865, -1, 7421, -1, 1293, -1, 8201, -1], 'generators': [944, 1332], 'label': '1944.2466.72.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.m1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.m1.a1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 107441109
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '18.3', 'aut_weyl_index': 216, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.v1.a1', '24.b1.a1', '36.q1.a1'], 'contains': ['216.c1.a1', '216.f1.a1', '216.g1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3092, -1, 3065, -1, 4714, -1, 4444, -1], 'generators': [722, 6], 'label': '1944.2466.72.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '72.n1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.n1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 107441110
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '18.3', 'aut_weyl_index': 216, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.v1.b1', '24.b1.a1', '36.q1.b1'], 'contains': ['216.c1.b1', '216.f1.a1', '216.g1.a1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [3092, -1, 2889, -1, 4714, -1, 4519, -1], 'generators': [1334, 6], 'label': '1944.2466.72.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '72.n1.b1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.n1.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 107441111
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '18.3', 'aut_weyl_index': 216, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.f1.a1', '36.g1.a1', '36.r1.a1'], 'contains': ['216.c1.a1', '216.h1.a1', '216.i1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4626, -1, 9197, -1, 4356, -1, 5531, -1], 'generators': [722, 936], 'label': '1944.2466.72.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '72.o1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.o1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 107441112
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '18.3', 'aut_weyl_index': 216, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.f1.b1', '36.g1.b1', '36.r1.b1'], 'contains': ['216.c1.b1', '216.h1.a1', '216.i1.a1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [4626, -1, 9318, -1, 4356, -1, 5770, -1], 'generators': [1334, 936], 'label': '1944.2466.72.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '72.o1.b1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.o1.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 107441113
    {'ambient': '1944.2466', 'aut_centralizer_order': 27, 'aut_label': '72.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.2', 'aut_weyl_index': 648, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.x1.a1', '24.c1.a1', '36.s1.a1'], 'contains': ['216.c1.a1', '216.j1.a1', '216.k1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6116, -1, 4076, -1, 2759, -1, 9118, -1], 'generators': [722, 1122], 'label': '1944.2466.72.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '72.p1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.p1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107441114
    {'ambient': '1944.2466', 'aut_centralizer_order': 27, 'aut_label': '72.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.2', 'aut_weyl_index': 648, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.x1.b1', '24.c1.a1', '36.s1.b1'], 'contains': ['216.c1.b1', '216.j1.a1', '216.k1.a1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [6116, -1, 3516, -1, 2759, -1, 9261, -1], 'generators': [1334, 1122], 'label': '1944.2466.72.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '72.p1.b1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.p1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107441115
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '72.q1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '18.3', 'aut_weyl_index': 216, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.y1.a1', '24.d1.a1', '36.t1.a1'], 'contains': ['216.c1.a1', '216.l1.a1', '216.m1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9744, -1, 6117, -1, 675, -1, 7382, -1], 'generators': [722, 942], 'label': '1944.2466.72.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '72.q1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.q1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 107441116
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '72.q1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '18.3', 'aut_weyl_index': 216, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.y1.b1', '24.d1.a1', '36.t1.b1'], 'contains': ['216.c1.b1', '216.l1.a1', '216.m1.a1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [9744, -1, 5828, -1, 675, -1, 7736, -1], 'generators': [1334, 942], 'label': '1944.2466.72.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '72.q1.b1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.q1.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 107441117
    {'ambient': '1944.2466', 'aut_centralizer_order': 18, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.5', 'aut_weyl_index': 486, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1.a1', '27.b1.a1', '27.c1.a1'], 'contains': ['162.a1.a1', '162.c1.a1', '162.g1.a1', '243.a1.a1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [148, -1, 432, -1, 9076, -1, 995, -1], 'generators': [3, 972, 2, 54], 'label': '1944.2466.81.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': '81.a1.a1', 'projective_image': '648.278', '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': '4.2'}
  • id: 107441118
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '648.572', 'aut_weyl_index': 6, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['18.c1.a1', '18.r1.a1', '18.t1.a1', '18.u1.a1', '24.g1.a1'], 'core': '18.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7660, -1, 5243, -1, 2636, -1, 7406, -1], 'generators': [8, 972, 54, 936, 1332, 648], 'label': '1944.2466.6.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '6.i1.a1', 'projective_image': '1944.2466', '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': '108.22'}
  • id: 107441119
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '81.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 972, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1.a1', '27.d1.a1'], 'contains': ['162.d1.a1', '162.i1.a1', '162.l1.a1', '243.a1.a1'], 'core': '486.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1686, -1, 1430, -1, 8537, -1, 1776, -1], 'generators': [3, 972, 36, 54], 'label': '1944.2466.81.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '81.b1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 107441120
    {'ambient': '1944.2466', 'aut_centralizer_order': 18, 'aut_label': '81.c1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 972, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1.a1', '27.e1.a1'], 'contains': ['162.e1.a1', '162.j1.a1', '162.m1.a1', '243.a1.a1'], 'core': '486.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [683, -1, 819, -1, 8706, -1, 1139, -1], 'generators': [3, 972, 74, 54], 'label': '1944.2466.81.c1.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': '81.c1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 107441121
    {'ambient': '1944.2466', 'aut_centralizer_order': 18, 'aut_label': '81.c1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 972, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1.a1', '27.e1.b1'], 'contains': ['162.e1.b1', '162.j1.b1', '162.m1.b1', '243.a1.a1'], 'core': '486.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [683, -1, 1159, -1, 8706, -1, 1282, -1], 'generators': [3, 972, 38, 54], 'label': '1944.2466.81.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '81.c1.b1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.c1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 107441122
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '81.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.b1.a1', '27.d1.a1', '27.e1.a1', '27.e1.b1', '27.f1.a1', '27.g1.a1', '27.h1.a1', '27.i1.a1'], 'contains': ['162.b1.a1', '162.f1.a1', '162.h1.a1', '243.a1.a1'], 'core': '162.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3129, -1, 1925, -1, 7519, -1, 2682, -1], 'generators': [3, 972, 54, 648], 'label': '1944.2466.81.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '81.d1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107441123
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '81.e1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '24.12', 'aut_weyl_index': 162, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.c1.a1', '27.f1.a1'], 'contains': ['162.n1.a1', '243.a1.a1', '324.j1.a1'], 'core': '486.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [30, -1, 25, -1, 9966, -1, 28, -1], 'generators': [3, 6, 54, 972], 'label': '1944.2466.81.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1.a1', 'old_label': '81.e1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107441124
    {'ambient': '1944.2466', 'aut_centralizer_order': 324, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 972, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.b1.a1', '36.c1.a1', '54.a1.a1', '54.e1.a1', '54.i1.a1'], 'contains': ['216.a1.a1', '324.a1.a1', '324.b1.a1', '324.c1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3445, -1, 4364, -1, 6359, -1, 3786, -1], 'generators': [54, 2, 648], 'label': '1944.2466.108.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '108.a1.a1', 'projective_image': '648.278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107441125
    {'ambient': '1944.2466', 'aut_centralizer_order': 216, 'aut_label': '108.b1', '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': ['36.a1.a1', '54.d1.a1', '54.j1.a1', '54.n1.a1'], 'contains': ['216.d1.a1', '324.a1.a1', '324.d1.a1', '324.e1.a1', '324.e1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1428, -1, 1831, -1, 7029, -1, 3073, -1], 'generators': [54, 2, 1332], 'label': '1944.2466.108.b1.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': '108.b1.a1', 'projective_image': '648.278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107441126
    {'ambient': '1944.2466', 'aut_centralizer_order': 216, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.d1.a1', '36.e1.a1', '54.b1.a1', '54.f1.a1', '54.k1.a1'], 'contains': ['216.b1.a1', '324.b1.a1', '324.d1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4017, -1, 5656, -1, 5625, -1, 4628, -1], 'generators': [54, 1332, 648], 'label': '1944.2466.108.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '108.c1.a1', 'projective_image': '1944.2466', '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': '6.1'}
  • id: 107441127
    {'ambient': '1944.2466', 'aut_centralizer_order': 108, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.f1.a1', '36.g1.a1', '54.c1.a1', '54.g1.a1', '54.l1.a1'], 'contains': ['216.c1.a1', '324.b1.a1', '324.e1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2887, -1, 4813, -1, 6102, -1, 4004, -1], 'generators': [54, 722, 648], 'label': '1944.2466.108.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '108.d1.a1', 'projective_image': '1944.2466', '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': '6.1'}
  • id: 107441128
    {'ambient': '1944.2466', 'aut_centralizer_order': 108, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.f1.b1', '36.g1.b1', '54.c1.b1', '54.g1.b1', '54.l1.b1'], 'contains': ['216.c1.b1', '324.b1.a1', '324.e1.b1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [2887, -1, 4651, -1, 6102, -1, 4146, -1], 'generators': [54, 1334, 648], 'label': '1944.2466.108.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '108.d1.b1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107441129
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '6.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '648.572', 'aut_weyl_index': 6, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['18.d1.a1', '18.r1.a1', '18.s1.a1', '18.u1.a1', '24.h1.a1'], 'core': '18.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8421, -1, 4850, -1, 2937, -1, 7661, -1], 'generators': [938, 972, 54, 1122, 36, 648], 'label': '1944.2466.6.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '6.j1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.j1.a1', 'subgroup_fusion': None, 'weyl_group': '108.22'}
  • id: 107441130
    {'ambient': '1944.2466', 'aut_centralizer_order': 216, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.2', 'aut_weyl_index': 648, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.d1.a1', '36.f1.a1', '36.f1.b1', '54.h1.a1', '54.m1.a1', '54.r1.a1'], 'contains': ['216.h1.a1', '324.b1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3892, -1, 8799, -1, 5949, -1, 4360, -1], 'generators': [54, 936, 648], 'label': '1944.2466.108.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '108.e1.a1', 'projective_image': '1944.2466', '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': '6.2'}
  • id: 107441131
    {'ambient': '1944.2466', 'aut_centralizer_order': 216, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '3.1', 'aut_weyl_index': 1296, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '36.d1.a1', '36.g1.a1', '36.g1.b1', '54.r1.a1'], 'contains': ['216.h1.a1', '324.b1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4202, -1, 8395, -1, 5478, -1, 5150, -1], 'generators': [972, 936, 648], 'label': '1944.2466.108.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '108.f1.a1', 'projective_image': '1944.2466', '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': '3.1'}
  • id: 107441132
    {'ambient': '1944.2466', 'aut_centralizer_order': 108, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 648, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.e1.a1', '36.g1.a1', '36.g1.b1', '54.s1.a1'], 'contains': ['216.i1.a1', '324.b1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4389, -1, 7634, -1, 5261, -1, 5336, -1], 'generators': [54, 938, 648], 'label': '1944.2466.108.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '108.g1.a1', 'projective_image': '1944.2466', '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': '3.1'}
  • id: 107441133
    {'ambient': '1944.2466', 'aut_centralizer_order': 108, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '3.1', 'aut_weyl_index': 1296, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '36.e1.a1', '36.f1.b1', '36.g1.a1', '54.s1.a1'], 'contains': ['216.i1.a1', '324.b1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4644, -1, 7716, -1, 5369, -1, 5244, -1], 'generators': [1026, 938, 648], 'label': '1944.2466.108.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '108.h1.a1', 'projective_image': '1944.2466', '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': '3.1'}
  • id: 107441134
    {'ambient': '1944.2466', 'aut_centralizer_order': 108, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '3.1', 'aut_weyl_index': 1296, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '36.e1.a1', '36.f1.a1', '36.g1.b1', '54.s1.a1'], 'contains': ['216.i1.a1', '324.b1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4644, -1, 7940, -1, 5369, -1, 5437, -1], 'generators': [972, 938, 648], 'label': '1944.2466.108.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '108.h1.b1', 'projective_image': '1944.2466', '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': '3.1'}
  • id: 107441135
    {'ambient': '1944.2466', 'aut_centralizer_order': 108, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '54.x1.a1'], 'contains': ['216.n1.a1', '324.c1.a1', '324.d1.a1', '324.e1.a1', '324.e1.b1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3597, -1, 3159, -1, 6526, -1, 3358, -1], 'generators': [54, 650, 1332], 'label': '1944.2466.108.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '108.i1.a1', 'projective_image': '1944.2466', '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': '1.1'}
  • id: 107441136
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '108.j1', '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.h1.a1', '54.d1.a1'], 'contains': ['216.d1.a1', '324.f1.a1', '324.g1.a1', '324.h1.a1', '324.h1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [3166, -1, 4202, -1, 4842, -1, 4913, -1], 'generators': [3, 2, 36], 'label': '1944.2466.108.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1.a1', 'old_label': '108.j1.a1', 'projective_image': '648.278', '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': '1.1'}
  • id: 107441137
    {'ambient': '1944.2466', 'aut_centralizer_order': 18, 'aut_label': '108.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': ['36.h1.a1', '36.i1.a1', '36.j1.a1', '36.k1.a1', '36.l1.a1', '54.e1.a1'], 'contains': ['216.a1.a1', '324.f1.a1', '324.i1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6022, -1, 4526, -1, 4216, -1, 5964, -1], 'generators': [3, 2, 648], 'label': '1944.2466.108.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '108.k1.a1', 'projective_image': '648.278', '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: 107441138
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '108.l1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.c1.a1', '36.i1.a1'], 'contains': ['216.e1.a1', '324.f1.a1', '324.j1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [1021, -1, 785, -1, 8791, -1, 1370, -1], 'generators': [3, 2, 6], 'label': '1944.2466.108.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.l1.a1', 'old_label': '108.l1.a1', 'projective_image': '648.278', '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: 107441139
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '36.m1.a1', '36.n1.a1', '36.o1.a1', '36.p1.a1', '54.f1.a1'], 'contains': ['216.b1.a1', '324.g1.a1', '324.i1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6651, -1, 6591, -1, 3103, -1, 6686, -1], 'generators': [3, 1332, 648], 'label': '1944.2466.108.m1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '108.m1.a1', 'projective_image': '1944.2466', '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': '6.1'}
  • id: 107441140
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '6.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '648.572', 'aut_weyl_index': 6, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['18.e1.a1', '18.r1.a1', '18.s1.a1', '18.t1.a1', '24.i1.a1'], 'core': '18.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8796, -1, 4638, -1, 2486, -1, 7534, -1], 'generators': [938, 972, 54, 942, 684, 648], 'label': '1944.2466.6.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '6.k1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.k1.a1', 'subgroup_fusion': None, 'weyl_group': '108.22'}
  • id: 107441141
    {'ambient': '1944.2466', 'aut_centralizer_order': 18, 'aut_label': '108.n1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '36.q1.a1', '36.r1.a1', '36.s1.a1', '36.t1.a1', '54.g1.a1'], 'contains': ['216.c1.a1', '324.h1.a1', '324.i1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5395, -1, 5919, -1, 4050, -1, 6106, -1], 'generators': [3, 722, 648], 'label': '1944.2466.108.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '108.n1.a1', 'projective_image': '1944.2466', '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: 107441142
    {'ambient': '1944.2466', 'aut_centralizer_order': 18, 'aut_label': '108.n1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '36.q1.b1', '36.r1.b1', '36.s1.b1', '36.t1.b1', '54.g1.b1'], 'contains': ['216.c1.b1', '324.h1.b1', '324.i1.a1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [5395, -1, 5529, -1, 4050, -1, 6247, -1], 'generators': [3, 1334, 648], 'label': '1944.2466.108.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '108.n1.b1', 'projective_image': '1944.2466', '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: 107441143
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '108.o1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '54.5', 'aut_weyl_index': 72, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.f1.a1', '36.i1.a1', '36.m1.a1', '36.q1.a1', '36.q1.b1'], 'contains': ['216.f1.a1', '324.i1.a1', '324.j1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2505, -1, 2983, -1, 5150, -1, 4265, -1], 'generators': [3, 6, 648], 'label': '1944.2466.108.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '108.o1.a1', 'projective_image': '1944.2466', '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': '54.5'}
  • id: 107441144
    {'ambient': '1944.2466', 'aut_centralizer_order': 12, 'aut_label': '108.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '54.6', 'aut_weyl_index': 72, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1.a1', '36.n1.a1', '36.r1.a1', '36.r1.b1', '54.h1.a1'], 'contains': ['216.h1.a1', '324.i1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5109, -1, 9449, -1, 4457, -1, 5856, -1], 'generators': [3, 936, 648], 'label': '1944.2466.108.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '108.p1.a1', 'projective_image': '1944.2466', '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': '54.6'}
  • id: 107441145
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '108.q1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '54.6', 'aut_weyl_index': 72, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.h1.a1', '36.k1.a1', '36.o1.a1', '36.s1.a1', '36.s1.b1'], 'contains': ['216.j1.a1', '324.i1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6163, -1, 3751, -1, 3537, -1, 9559, -1], 'generators': [3, 1806, 648], 'label': '1944.2466.108.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '108.q1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.q1.a1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 107441146
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '108.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '54.6', 'aut_weyl_index': 72, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.i1.a1', '36.l1.a1', '36.p1.a1', '36.t1.a1', '36.t1.b1'], 'contains': ['216.l1.a1', '324.i1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9259, -1, 5752, -1, 574, -1, 7508, -1], 'generators': [3, 906, 648], 'label': '1944.2466.108.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '108.r1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.r1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 107441147
    {'ambient': '1944.2466', 'aut_centralizer_order': 324, 'aut_label': '162.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '6.b1.a1', 'complements': ['12.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['54.a1.a1', '54.n1.a1', '54.o1.a1', '81.a1.a1'], 'contains': ['324.a1.a1', '486.a1.a1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1478, 1405, 359, 9224, 8197, 1907, 2036, 9438], 'generators': [54, 972, 2], 'label': '1944.2466.162.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '162.a1.a1', 'normal_contained_in': ['54.a1.a1'], 'normal_contains': ['486.a1.a1', '648.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '162.a1.a1', 'projective_image': '648.278', 'quotient_action_image': '6.1', 'quotient_action_kernel': '27.4', 'quotient_action_kernel_order': 27, 'quotient_fusion': None, 'short_label': '162.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107441148
    {'ambient': '1944.2466', 'aut_centralizer_order': 648, 'aut_label': '162.b1', 'aut_quo_index': 72, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['54.a1.a1', '54.b1.a1', '54.c1.a1', '54.c1.b1', '54.p1.a1', '54.q1.a1', '54.r1.a1', '54.s1.a1', '54.t1.a1', '54.u1.a1', '54.v1.a1', '54.w1.a1', '81.d1.a1'], 'contains': ['324.b1.a1', '486.a1.a1'], 'core': '162.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5606, 3242, 2300, 7412, 5009, 3268, 4770, 6578], 'generators': [54, 972, 648], 'label': '1944.2466.162.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '162.b1.a1', 'normal_contained_in': ['54.a1.a1', '54.c1.b1', '54.c1.a1', '54.b1.a1'], 'normal_contains': ['486.a1.a1', '648.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '162.b1.a1', 'projective_image': '1944.2466', 'quotient_action_image': '6.1', 'quotient_action_kernel': '27.5', 'quotient_action_kernel_order': 27, 'quotient_fusion': None, 'short_label': '162.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107441149
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '162.c1', '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': ['54.d1.a1', '54.e1.a1', '81.a1.a1'], 'contains': ['324.a1.a1', '324.f1.a1', '486.b1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [920, -1, 2068, -1, 7196, -1, 2703, -1], 'generators': [3, 54, 2], 'label': '1944.2466.162.c1.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': '162.c1.a1', 'projective_image': '648.278', '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': '2.1'}
  • id: 107441150
    {'ambient': '1944.2466', 'aut_centralizer_order': 72, 'aut_label': '162.d1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '54.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.d1.a1', '54.f1.a1', '81.b1.a1'], 'contains': ['324.d1.a1', '324.g1.a1', '486.b1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [2039, -1, 2659, -1, 6694, -1, 3643, -1], 'generators': [3, 54, 36], 'label': '1944.2466.162.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '162.d1.a1', 'projective_image': '1944.2466', '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': '2.1'}
  • id: 107441151
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1296.3002', 'aut_weyl_index': 3, 'centralizer': '216.a1.a1', 'complements': ['972.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '6.d1.a1', '6.e1.a1', '6.h1.a1', '6.i1.a1', '6.j1.a1', '6.k1.a1', '8.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7660, 5226, 5065, 4631, 2937, 4700, 7278, 3527], 'generators': [2, 54, 648, 6, 972, 936, 1332], 'label': '1944.2466.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '6.d1.a1', '6.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '648.278', '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': '216.95'}
  • id: 107441152
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '324.145', 'aut_weyl_index': 12, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.a1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.c1.a1', '24.d1.a1', '24.e1.a1', '24.f1.a1', '24.g1.a1', '24.h1.a1', '24.i1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8083, -1, 6502, -1, 1655, -1, 8162, -1], 'generators': [2, 6, 936], 'label': '1944.2466.8.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '648.278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '54.8'}
  • id: 107441153
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '162.e1', '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': ['54.d1.a1', '54.g1.a1', '81.c1.a1'], 'contains': ['324.e1.a1', '324.h1.a1', '486.b1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1114, -1, 2533, -1, 6861, -1, 3216, -1], 'generators': [3, 54, 74], 'label': '1944.2466.162.e1.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': '162.e1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107441154
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '162.e1', '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': ['54.d1.a1', '54.g1.b1', '81.c1.b1'], 'contains': ['324.e1.b1', '324.h1.b1', '486.b1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1114, -1, 2786, -1, 6861, -1, 3501, -1], 'generators': [3, 54, 38], 'label': '1944.2466.162.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '162.e1.b1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.e1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107441155
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '162.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.e1.a1', '54.f1.a1', '54.g1.a1', '54.g1.b1', '54.h1.a1', '81.d1.a1'], 'contains': ['324.b1.a1', '324.i1.a1', '486.b1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2919, -1, 5374, -1, 6230, -1, 3895, -1], 'generators': [3, 54, 648], 'label': '1944.2466.162.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '162.f1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107441156
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '162.g1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 972, 'centralizer': '54.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.i1.a1', '54.j1.a1', '81.a1.a1'], 'contains': ['324.a1.a1', '486.c1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [245, -1, 884, -1, 8424, -1, 1567, -1], 'generators': [975, 2, 54], 'label': '1944.2466.162.g1.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': '162.g1.a1', 'projective_image': '648.278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107441157
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '162.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.i1.a1', '54.k1.a1', '54.l1.a1', '54.l1.b1', '54.m1.a1', '81.d1.a1'], 'contains': ['324.b1.a1', '486.c1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1912, -1, 3493, -1, 7840, -1, 2156, -1], 'generators': [975, 54, 648], 'label': '1944.2466.162.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '162.h1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107441158
    {'ambient': '1944.2466', 'aut_centralizer_order': 72, 'aut_label': '162.i1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '54.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.j1.a1', '54.k1.a1', '81.b1.a1'], 'contains': ['324.d1.a1', '486.c1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1768, -1, 1573, -1, 7950, -1, 1919, -1], 'generators': [975, 36, 54], 'label': '1944.2466.162.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '162.i1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107441159
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '162.j1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '54.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.j1.a1', '54.l1.a1', '81.c1.a1'], 'contains': ['324.e1.a1', '486.c1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [457, -1, 1238, -1, 8059, -1, 1659, -1], 'generators': [975, 74, 54], 'label': '1944.2466.162.j1.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': '162.j1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107441160
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '162.j1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '54.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.j1.a1', '54.l1.b1', '81.c1.b1'], 'contains': ['324.e1.b1', '486.c1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [457, -1, 1655, -1, 8059, -1, 1827, -1], 'generators': [975, 38, 54], 'label': '1944.2466.162.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '162.j1.b1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.j1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107441161
    {'ambient': '1944.2466', 'aut_centralizer_order': 324, 'aut_label': '162.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1.a1', '54.x1.a1', '54.y1.a1'], 'contains': ['324.c1.a1', '486.a1.a1'], 'core': '486.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4936, -1, 1941, -1, 7364, -1, 2418, -1], 'generators': [54, 972, 650], 'label': '1944.2466.162.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '162.k1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.k1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 107441162
    {'ambient': '1944.2466', 'aut_centralizer_order': 216, 'aut_label': '162.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.b1.a1', '54.n1.a1', '54.x1.a1', '81.b1.a1'], 'contains': ['324.d1.a1', '486.a1.a1'], 'core': '486.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3289, -1, 1468, -1, 7532, -1, 2931, -1], 'generators': [54, 972, 1332], 'label': '1944.2466.162.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '162.l1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.l1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107441163
    {'ambient': '1944.2466', 'aut_centralizer_order': 18, 'aut_label': '9.a1', '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': ['3.b1.a1', '3.c1.a1', '3.d1.a1', '3.e1.a1'], 'contains': ['18.a1.a1', '18.f1.a1', '18.j1.a1', '27.a1.a1', '27.b1.a1', '27.d1.a1', '27.e1.a1', '27.e1.b1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1984, -1, 2516, -1, 6769, -1, 3196, -1], 'generators': [3, 648, 54, 972, 2, 1332], 'label': '1944.2466.9.a1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '648.278', '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': '12.4'}
  • id: 107441164
    {'ambient': '1944.2466', 'aut_centralizer_order': 108, 'aut_label': '162.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1.a1', '54.n1.a1', '54.x1.a1', '81.c1.a1'], 'contains': ['324.e1.a1', '486.a1.a1'], 'core': '486.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4783, -1, 1132, -1, 7699, -1, 2275, -1], 'generators': [54, 972, 722], 'label': '1944.2466.162.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '162.m1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.m1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107441165
    {'ambient': '1944.2466', 'aut_centralizer_order': 108, 'aut_label': '162.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1.b1', '54.n1.a1', '54.x1.a1', '81.c1.b1'], 'contains': ['324.e1.b1', '486.a1.a1'], 'core': '486.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4783, -1, 1342, -1, 7699, -1, 2560, -1], 'generators': [54, 972, 1334], 'label': '1944.2466.162.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '162.m1.b1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.m1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107441166
    {'ambient': '1944.2466', 'aut_centralizer_order': 18, 'aut_label': '162.n1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.12', 'aut_weyl_index': 162, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.o1.a1', '54.p1.a1', '54.y1.a1', '81.e1.a1'], 'contains': ['486.a1.a1', '648.f1.a1'], 'core': '486.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [352, -1, 136, -1, 9517, -1, 410, -1], 'generators': [6, 54, 972], 'label': '1944.2466.162.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '162.n1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.n1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107441167
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '162.o1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.12', 'aut_weyl_index': 162, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.o1.a1', '54.q1.a1', '54.y1.a1'], 'contains': ['486.a1.a1', '648.g1.a1'], 'core': '486.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1594, -1, 263, -1, 8663, -1, 682, -1], 'generators': [8, 54, 972], 'label': '1944.2466.162.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1.a1', 'old_label': '162.o1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.o1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 107441168
    {'ambient': '1944.2466', 'aut_centralizer_order': 972, 'aut_label': '216.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 972, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.c1.a1', '72.d1.a1', '72.e1.a1', '72.f1.a1', '108.a1.a1', '108.k1.a1'], 'contains': ['648.a1.a1', '648.b1.a1', '648.c1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5716, 3876, 4353, 7443, 4356, 4359, 5752, 8399], 'generators': [2, 648], 'label': '1944.2466.216.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '216.a1.a1', 'normal_contained_in': ['54.a1.a1', '72.a1.a1'], 'normal_contains': ['648.a1.a1', '648.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.a1.a1', 'projective_image': '648.278', 'quotient_action_image': '2.1', 'quotient_action_kernel': '108.22', 'quotient_action_kernel_order': 108, 'quotient_fusion': None, 'short_label': '216.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107441169
    {'ambient': '1944.2466', 'aut_centralizer_order': 648, 'aut_label': '216.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '6.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.b1.a1', '72.g1.a1', '72.h1.a1', '72.i1.a1', '72.j1.a1', '72.k1.a1', '72.l1.a1', '72.m1.a1', '108.c1.a1', '108.m1.a1'], 'contains': ['648.b1.a1', '648.d1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7511, 5892, 7075, 4266, 2416, 6001, 7480, 4757], 'generators': [1332, 648], 'label': '1944.2466.216.b1.a1', 'mobius_quo': 0, 'mobius_sub': -108, 'normal_closure': '216.b1.a1', 'normal_contained_in': ['54.b1.a1', '72.a1.a1', '72.b1.a1'], 'normal_contains': ['648.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.b1.a1', 'projective_image': '1944.2466', 'quotient_action_image': '6.1', 'quotient_action_kernel': '36.11', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '216.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107441170
    {'ambient': '1944.2466', 'aut_centralizer_order': 324, 'aut_label': '216.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '6.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.n1.a1', '72.o1.a1', '72.p1.a1', '72.q1.a1', '108.d1.a1', '108.n1.a1'], 'contains': ['648.b1.a1', '648.e1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5270, 4741, 6106, 5255, 4167, 5180, 5871, 7617], 'generators': [722, 648], 'label': '1944.2466.216.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '216.c1.a1', 'normal_contained_in': ['54.c1.a1', '72.a1.a1'], 'normal_contains': ['648.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.c1.a1', 'projective_image': '1944.2466', 'quotient_action_image': '6.1', 'quotient_action_kernel': '36.11', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '216.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107441171
    {'ambient': '1944.2466', 'aut_centralizer_order': 324, 'aut_label': '216.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '6.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.n1.b1', '72.o1.b1', '72.p1.b1', '72.q1.b1', '108.d1.b1', '108.n1.b1'], 'contains': ['648.b1.a1', '648.e1.b1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5270, 4741, 5724, 6110, 4167, 5180, 6041, 5539], 'generators': [1334, 648], 'label': '1944.2466.216.c1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '216.c1.b1', 'normal_contained_in': ['54.c1.b1', '72.a1.a1'], 'normal_contains': ['648.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.c1.b1', 'projective_image': '1944.2466', 'quotient_action_image': '6.1', 'quotient_action_kernel': '36.11', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '216.c1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107441172
    {'ambient': '1944.2466', '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': '3.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '108.b1.a1', '108.j1.a1'], 'contains': ['648.a1.a1', '648.d1.a1', '648.e1.a1', '648.e1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3645, -1, 4096, -1, 5469, -1, 4704, -1], 'generators': [2, 1332], 'label': '1944.2466.216.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '216.d1.a1', 'projective_image': '648.278', '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': '1.1'}
  • id: 107441173
    {'ambient': '1944.2466', 'aut_centralizer_order': 27, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 972, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.o1.a1', '72.c1.a1', '108.l1.a1'], 'contains': ['648.a1.a1', '648.f1.a1', '648.g1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1636, -1, 1194, -1, 8171, -1, 1795, -1], 'generators': [2, 6], 'label': '1944.2466.216.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1.a1', 'old_label': '216.e1.a1', 'projective_image': '648.278', '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: 107441174
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '432.535', 'aut_weyl_index': 9, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['18.n1.a1', '27.b1.a1', '27.c1.a1', '27.f1.a1', '36.i1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [993, -1, 656, -1, 8436, -1, 1512, -1], 'generators': [3, 972, 54, 2, 6, 648], 'label': '1944.2466.9.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '9.b1.a1', 'projective_image': '648.278', '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': '216.92'}
  • id: 107441175
    {'ambient': '1944.2466', 'aut_centralizer_order': 54, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.2', 'aut_weyl_index': 648, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.p1.a1', '72.c1.a1', '72.g1.a1', '72.n1.a1', '72.n1.b1', '108.o1.a1'], 'contains': ['648.b1.a1', '648.f1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2662, -1, 3078, -1, 5760, -1, 4306, -1], 'generators': [6, 648], 'label': '1944.2466.216.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '216.f1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 107441176
    {'ambient': '1944.2466', 'aut_centralizer_order': 27, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.2', 'aut_weyl_index': 648, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.q1.a1', '72.c1.a1', '72.h1.a1', '72.n1.a1', '72.n1.b1'], 'contains': ['648.b1.a1', '648.g1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2571, -1, 3003, -1, 5570, -1, 4392, -1], 'generators': [8, 648], 'label': '1944.2466.216.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.b1.a1', 'old_label': '216.g1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.g1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 107441177
    {'ambient': '1944.2466', 'aut_centralizer_order': 216, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.2', 'aut_weyl_index': 648, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '72.d1.a1', '72.o1.a1', '72.o1.b1', '108.e1.a1', '108.f1.a1', '108.p1.a1'], 'contains': ['648.b1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4309, -1, 9134, -1, 4540, -1, 5654, -1], 'generators': [936], 'label': '1944.2466.216.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '216.h1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 107441178
    {'ambient': '1944.2466', 'aut_centralizer_order': 108, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 648, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '72.i1.a1', '72.o1.a1', '72.o1.b1', '108.g1.a1', '108.h1.a1', '108.h1.b1'], 'contains': ['648.b1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4389, -1, 7599, -1, 4451, -1, 5553, -1], 'generators': [938], 'label': '1944.2466.216.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '216.i1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.i1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 107441179
    {'ambient': '1944.2466', 'aut_centralizer_order': 54, 'aut_label': '216.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.2', 'aut_weyl_index': 648, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.t1.a1', '72.e1.a1', '72.j1.a1', '72.p1.a1', '72.p1.b1', '108.q1.a1'], 'contains': ['648.b1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7023, -1, 3671, -1, 3473, -1, 9118, -1], 'generators': [1122], 'label': '1944.2466.216.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '216.j1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107441180
    {'ambient': '1944.2466', 'aut_centralizer_order': 27, 'aut_label': '216.k1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.2', 'aut_weyl_index': 648, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.u1.a1', '72.e1.a1', '72.k1.a1', '72.p1.a1', '72.p1.b1'], 'contains': ['648.b1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7362, -1, 3604, -1, 3302, -1, 8981, -1], 'generators': [950], 'label': '1944.2466.216.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '216.k1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107441181
    {'ambient': '1944.2466', 'aut_centralizer_order': 54, 'aut_label': '216.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.2', 'aut_weyl_index': 648, 'centralizer': '72.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.v1.a1', '72.f1.a1', '72.l1.a1', '72.q1.a1', '72.q1.b1', '108.r1.a1'], 'contains': ['648.b1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9367, -1, 5895, -1, 715, -1, 7400, -1], 'generators': [942], 'label': '1944.2466.216.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '216.l1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.l1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 107441182
    {'ambient': '1944.2466', 'aut_centralizer_order': 27, 'aut_label': '216.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.2', 'aut_weyl_index': 648, 'centralizer': '72.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.w1.a1', '72.f1.a1', '72.m1.a1', '72.q1.a1', '72.q1.b1'], 'contains': ['648.b1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9637, -1, 6235, -1, 941, -1, 7598, -1], 'generators': [944], 'label': '1944.2466.216.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1.a1', 'old_label': '216.m1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.m1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 107441183
    {'ambient': '1944.2466', 'aut_centralizer_order': 324, 'aut_label': '216.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '108.i1.a1'], 'contains': ['648.c1.a1', '648.d1.a1', '648.e1.a1', '648.e1.b1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4875, -1, 4465, -1, 5279, -1, 4790, -1], 'generators': [650, 1332], 'label': '1944.2466.216.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '216.n1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.n1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107441184
    {'ambient': '1944.2466', 'aut_centralizer_order': 27, 'aut_label': '216.o1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.y1.a1', '72.c1.a1'], 'contains': ['648.c1.a1', '648.f1.a1', '648.g1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1932, -1, 1599, -1, 7935, -1, 1881, -1], 'generators': [650, 6], 'label': '1944.2466.216.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.c1.a1', 'old_label': '216.o1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.o1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107441185
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '9.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '216.111', 'aut_weyl_index': 18, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.a1'], 'contains': ['18.g1.a1', '18.k1.a1', '18.o1.a1', '27.b1.a1', '27.g1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2840, -1, 8364, -1, 6550, -1, 3595, -1], 'generators': [3, 648, 936, 972, 2, 54], 'label': '1944.2466.9.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '9.c1.a1', 'projective_image': '648.278', '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': '108.26'}
  • id: 107441186
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '243.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 972, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['81.a1.a1', '81.b1.a1', '81.c1.a1', '81.c1.b1', '81.d1.a1', '81.e1.a1'], 'contains': ['486.a1.a1', '486.b1.a1', '486.c1.a1'], 'core': '486.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [833, -1, 668, -1, 8325, -1, 1743, -1], 'generators': [3, 972], 'label': '1944.2466.243.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '243.a1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 107441187
    {'ambient': '1944.2466', 'aut_centralizer_order': 648, 'aut_label': '324.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '3.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '108.b1.a1', '162.a1.a1', '162.c1.a1', '162.g1.a1'], 'contains': ['648.a1.a1', '972.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1320, -1, 1739, -1, 7029, -1, 3073, -1], 'generators': [54, 2], 'label': '1944.2466.324.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '162.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '324.a1.a1', 'projective_image': '648.278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107441188
    {'ambient': '1944.2466', 'aut_centralizer_order': 648, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '108.c1.a1', '108.d1.a1', '108.d1.b1', '108.e1.a1', '108.f1.a1', '108.g1.a1', '108.h1.a1', '108.h1.b1', '162.b1.a1', '162.f1.a1', '162.h1.a1'], 'contains': ['648.b1.a1', '972.a1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3930, -1, 5692, -1, 5948, -1, 4473, -1], 'generators': [54, 648], 'label': '1944.2466.324.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '162.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '324.b1.a1', 'projective_image': '1944.2466', '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': '2.1'}
  • id: 107441189
    {'ambient': '1944.2466', 'aut_centralizer_order': 324, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '108.i1.a1', '162.k1.a1'], 'contains': ['648.c1.a1', '972.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4548, -1, 3750, -1, 6526, -1, 3291, -1], 'generators': [54, 650], 'label': '1944.2466.324.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '324.c1.a1', 'projective_image': '1944.2466', '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: 107441190
    {'ambient': '1944.2466', 'aut_centralizer_order': 432, 'aut_label': '324.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3888, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.b1.a1', '108.c1.a1', '108.i1.a1', '162.d1.a1', '162.i1.a1', '162.l1.a1'], 'contains': ['648.d1.a1', '972.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2979, -1, 2451, -1, 6686, -1, 3528, -1], 'generators': [54, 1332], 'label': '1944.2466.324.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '324.d1.a1', 'projective_image': '1944.2466', '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: 107441191
    {'ambient': '1944.2466', 'aut_centralizer_order': 216, 'aut_label': '324.e1', '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.b1.a1', '108.d1.a1', '108.i1.a1', '162.e1.a1', '162.j1.a1', '162.m1.a1'], 'contains': ['648.e1.a1', '972.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2079, -1, 1883, -1, 6775, -1, 3216, -1], 'generators': [54, 722], 'label': '1944.2466.324.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '324.e1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107441192
    {'ambient': '1944.2466', 'aut_centralizer_order': 216, 'aut_label': '324.e1', '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.b1.a1', '108.d1.b1', '108.i1.a1', '162.e1.b1', '162.j1.b1', '162.m1.b1'], 'contains': ['648.e1.b1', '972.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2079, -1, 2602, -1, 6775, -1, 3367, -1], 'generators': [54, 1334], 'label': '1944.2466.324.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '324.e1.b1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107441193
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '324.f1', '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': ['108.j1.a1', '108.k1.a1', '108.l1.a1', '162.c1.a1'], 'contains': ['648.a1.a1', '972.b1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [2159, -1, 3408, -1, 5855, -1, 4226, -1], 'generators': [3, 2], 'label': '1944.2466.324.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1.a1', 'old_label': '324.f1.a1', 'projective_image': '648.278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107441194
    {'ambient': '1944.2466', 'aut_centralizer_order': 72, 'aut_label': '324.g1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3888, 'centralizer': '54.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.j1.a1', '108.m1.a1', '162.d1.a1'], 'contains': ['648.d1.a1', '972.b1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [3461, -1, 3922, -1, 5374, -1, 4871, -1], 'generators': [3, 36], 'label': '1944.2466.324.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1.a1', 'old_label': '324.g1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107441195
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '324.h1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3888, 'centralizer': '54.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.j1.a1', '108.n1.a1', '162.e1.a1'], 'contains': ['648.e1.a1', '972.b1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [3541, -1, 3989, -1, 5665, -1, 4548, -1], 'generators': [3, 74], 'label': '1944.2466.324.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1.a1', 'old_label': '324.h1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107441196
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '9.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '432.533', 'aut_weyl_index': 9, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.d1.a1'], 'contains': ['18.p1.a1', '27.b1.a1', '27.h1.a1', '36.k1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5632, -1, 1509, -1, 4316, -1, 8946, -1], 'generators': [3, 972, 54, 2, 1806, 648], 'label': '1944.2466.9.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '9.d1.a1', 'projective_image': '648.278', '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': '72.15'}
  • id: 107441197
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '324.h1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3888, 'centralizer': '54.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.j1.a1', '108.n1.b1', '162.e1.b1'], 'contains': ['648.e1.b1', '972.b1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [3541, -1, 4202, -1, 5665, -1, 4624, -1], 'generators': [3, 38], 'label': '1944.2466.324.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1.a1', 'old_label': '324.h1.b1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.h1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107441198
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '324.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.k1.a1', '108.m1.a1', '108.n1.a1', '108.n1.b1', '108.o1.a1', '108.p1.a1', '108.q1.a1', '108.r1.a1', '162.f1.a1'], 'contains': ['648.b1.a1', '972.b1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5414, -1, 5426, -1, 4261, -1, 5960, -1], 'generators': [3, 648], 'label': '1944.2466.324.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '324.i1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107441199
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '324.j1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['81.e1.a1', '108.l1.a1', '108.o1.a1'], 'contains': ['648.f1.a1', '972.b1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [1602, -1, 1285, -1, 8076, -1, 1962, -1], 'generators': [3, 6], 'label': '1944.2466.324.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.l1.a1', 'old_label': '324.j1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107441200
    {'ambient': '1944.2466', 'aut_centralizer_order': 648, 'aut_label': '486.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 648, 'centralizer': '6.b1.a1', 'complements': ['4.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['162.a1.a1', '162.b1.a1', '162.k1.a1', '162.l1.a1', '162.m1.a1', '162.m1.b1', '162.n1.a1', '162.o1.a1', '243.a1.a1'], 'contains': ['972.a1.a1'], 'core': '486.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2358, 2609, 1040, 8151, 7699, 3068, 2346, 7579], 'generators': [54, 972], 'label': '1944.2466.486.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '486.a1.a1', 'normal_contained_in': ['162.a1.a1', '162.b1.a1'], 'normal_contains': ['1944.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '486.a1.a1', 'projective_image': '1944.2466', 'quotient_action_image': '6.1', 'quotient_action_kernel': '81.13', 'quotient_action_kernel_order': 81, 'quotient_fusion': None, 'short_label': '486.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107441201
    {'ambient': '1944.2466', 'aut_centralizer_order': 72, 'aut_label': '486.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '54.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.c1.a1', '162.d1.a1', '162.e1.a1', '162.e1.b1', '162.f1.a1', '243.a1.a1'], 'contains': ['972.a1.a1', '972.b1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1412, -1, 2779, -1, 6870, -1, 3447, -1], 'generators': [3, 54], 'label': '1944.2466.486.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '486.b1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107441202
    {'ambient': '1944.2466', 'aut_centralizer_order': 72, 'aut_label': '486.c1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '54.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.g1.a1', '162.h1.a1', '162.i1.a1', '162.j1.a1', '162.j1.b1', '243.a1.a1'], 'contains': ['972.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [985, -1, 1443, -1, 7840, -1, 2037, -1], 'generators': [975], 'label': '1944.2466.486.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '486.c1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107441203
    {'ambient': '1944.2466', 'aut_centralizer_order': 1944, 'aut_label': '648.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '1.a1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '216.d1.a1', '216.e1.a1', '324.a1.a1', '324.f1.a1'], 'contains': ['1944.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2164, 3263, 3637, 8308, 5855, 3839, 4312, 8399], 'generators': [2], 'label': '1944.2466.648.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '648.a1.a1', 'normal_contained_in': ['162.a1.a1', '216.a1.a1'], 'normal_contains': ['1944.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '648.a1.a1', 'projective_image': '648.278', 'quotient_action_image': '1.1', 'quotient_action_kernel': '648.278', 'quotient_action_kernel_order': 648, 'quotient_fusion': None, 'short_label': '648.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107441204
    {'ambient': '1944.2466', 'aut_centralizer_order': 1944, 'aut_label': '648.b1', 'aut_quo_index': 18, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '216.b1.a1', '216.c1.a1', '216.c1.b1', '216.f1.a1', '216.g1.a1', '216.h1.a1', '216.i1.a1', '216.j1.a1', '216.k1.a1', '216.l1.a1', '216.m1.a1', '324.b1.a1', '324.i1.a1'], 'contains': ['1944.a1.a1'], 'core': '648.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5374, 4045, 5692, 6485, 4309, 4560, 5871, 6673], 'generators': [648], 'label': '1944.2466.648.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '648.b1.a1', 'normal_contained_in': ['162.b1.a1', '216.a1.a1', '216.c1.b1', '216.c1.a1', '216.b1.a1'], 'normal_contains': ['1944.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '648.b1.a1', 'projective_image': '1944.2466', 'quotient_action_image': '2.1', 'quotient_action_kernel': '324.135', 'quotient_action_kernel_order': 324, 'quotient_fusion': None, 'short_label': '648.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107441205
    {'ambient': '1944.2466', 'aut_centralizer_order': 972, 'aut_label': '648.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '216.n1.a1', '216.o1.a1', '324.c1.a1'], 'contains': ['1944.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4536, -1, 3999, -1, 5677, -1, 4473, -1], 'generators': [650], 'label': '1944.2466.648.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '648.c1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107441206
    {'ambient': '1944.2466', 'aut_centralizer_order': 1296, 'aut_label': '648.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3888, 'centralizer': '3.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1.a1', '216.d1.a1', '216.n1.a1', '324.d1.a1', '324.g1.a1'], 'contains': ['1944.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3602, -1, 4066, -1, 5406, -1, 4784, -1], 'generators': [1332], 'label': '1944.2466.648.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '648.d1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107441207
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '9.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '432.533', 'aut_weyl_index': 9, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.e1.a1'], 'contains': ['18.q1.a1', '27.b1.a1', '27.i1.a1', '36.l1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9665, -1, 2827, -1, 938, -1, 6517, -1], 'generators': [3, 972, 54, 2, 906, 648], 'label': '1944.2466.9.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.e1.a1', 'old_label': '9.e1.a1', 'projective_image': '648.278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.e1.a1', 'subgroup_fusion': None, 'weyl_group': '216.90'}
  • id: 107441208
    {'ambient': '1944.2466', 'aut_centralizer_order': 648, 'aut_label': '648.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3888, 'centralizer': '3.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1.a1', '216.d1.a1', '216.n1.a1', '324.e1.a1', '324.h1.a1'], 'contains': ['1944.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3843, -1, 4139, -1, 5528, -1, 4625, -1], 'generators': [722], 'label': '1944.2466.648.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '648.e1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107441209
    {'ambient': '1944.2466', 'aut_centralizer_order': 648, 'aut_label': '648.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3888, 'centralizer': '3.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1.b1', '216.d1.a1', '216.n1.a1', '324.e1.b1', '324.h1.b1'], 'contains': ['1944.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3843, -1, 4232, -1, 5528, -1, 4702, -1], 'generators': [1334], 'label': '1944.2466.648.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '648.e1.b1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107441210
    {'ambient': '1944.2466', 'aut_centralizer_order': 54, 'aut_label': '648.f1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.n1.a1', '216.e1.a1', '216.f1.a1', '216.o1.a1', '324.j1.a1'], 'contains': ['1944.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1563, -1, 1343, -1, 8049, -1, 1960, -1], 'generators': [6], 'label': '1944.2466.648.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1.a1', 'old_label': '648.f1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107441211
    {'ambient': '1944.2466', 'aut_centralizer_order': 27, 'aut_label': '648.g1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1944, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.o1.a1', '216.e1.a1', '216.g1.a1', '216.o1.a1'], 'contains': ['1944.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1932, -1, 1276, -1, 7935, -1, 1881, -1], 'generators': [8], 'label': '1944.2466.648.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.c1.a1', 'old_label': '648.g1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107441212
    {'ambient': '1944.2466', 'aut_centralizer_order': 1296, 'aut_label': '972.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3888, 'centralizer': '3.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.a1.a1', '324.b1.a1', '324.c1.a1', '324.d1.a1', '324.e1.a1', '324.e1.b1', '486.a1.a1', '486.b1.a1', '486.c1.a1'], 'contains': ['1944.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2248, -1, 2495, -1, 6775, -1, 3329, -1], 'generators': [54], 'label': '1944.2466.972.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '486.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '972.a1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107441213
    {'ambient': '1944.2466', 'aut_centralizer_order': 72, 'aut_label': '972.b1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3888, 'centralizer': '54.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.f1.a1', '324.g1.a1', '324.h1.a1', '324.h1.b1', '324.i1.a1', '324.j1.a1', '486.b1.a1'], 'contains': ['1944.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [2886, -1, 3863, -1, 5766, -1, 4548, -1], 'generators': [3], 'label': '1944.2466.972.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.d1.a1', 'old_label': '972.b1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107441214
    {'ambient': '1944.2466', 'aut_centralizer_order': None, 'aut_label': '1944.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': ['648.a1.a1', '648.b1.a1', '648.c1.a1', '648.d1.a1', '648.e1.a1', '648.e1.b1', '648.f1.a1', '648.g1.a1', '972.a1.a1', '972.b1.a1'], 'contains': [], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2886, 3263, 3938, 7734, 5766, 3839, 4511, 7579], 'generators': [], 'label': '1944.2466.1944.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1944.a1.a1', 'normal_contained_in': ['486.a1.a1', '648.a1.a1', '648.b1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1944.a1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107441215
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '9.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '216.92', 'aut_weyl_index': 18, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.b1.a1'], 'contains': ['18.b1.a1', '27.d1.a1', '27.f1.a1', '36.m1.a1'], 'core': '18.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4771, -1, 2996, -1, 5836, -1, 5704, -1], 'generators': [3, 972, 54, 1332, 6, 648], 'label': '1944.2466.9.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '9.f1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.f1.a1', 'subgroup_fusion': None, 'weyl_group': '216.92'}
  • id: 107441216
    {'ambient': '1944.2466', 'aut_centralizer_order': 12, 'aut_label': '9.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '108.26', 'aut_weyl_index': 36, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.c1.a1'], 'contains': ['18.c1.a1', '18.h1.a1', '18.l1.a1', '27.d1.a1', '27.g1.a1'], 'core': '18.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3489, -1, 6143, -1, 6070, -1, 4199, -1], 'generators': [3, 648, 936, 972, 1332, 54], 'label': '1944.2466.9.g1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '9.g1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.g1.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 107441217
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '9.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '216.90', 'aut_weyl_index': 18, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.d1.a1'], 'contains': ['18.d1.a1', '27.d1.a1', '27.h1.a1', '36.o1.a1'], 'core': '18.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5841, -1, 3655, -1, 3696, -1, 8750, -1], 'generators': [3, 972, 54, 1332, 1806, 648], 'label': '1944.2466.9.h1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '9.h1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.h1.a1', 'subgroup_fusion': None, 'weyl_group': '72.15'}
  • id: 107441218
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '9.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '216.90', 'aut_weyl_index': 18, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.e1.a1'], 'contains': ['18.e1.a1', '27.d1.a1', '27.i1.a1', '36.p1.a1'], 'core': '18.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8950, -1, 3830, -1, 1493, -1, 6791, -1], 'generators': [3, 972, 54, 1332, 906, 648], 'label': '1944.2466.9.i1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.e1.a1', 'old_label': '9.i1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.i1.a1', 'subgroup_fusion': None, 'weyl_group': '216.90'}
  • id: 107441219
    {'ambient': '1944.2466', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1944.2468', 'aut_weyl_index': 2, 'centralizer': '648.a1.a1', 'complements': ['648.a1.a1', '648.c1.a1', '648.e1.b1', '648.e1.a1', '648.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.e1.a1', '9.f1.a1', '9.g1.a1', '9.h1.a1', '9.i1.a1', '12.f1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6280, 6790, 4014, 3245, 3322, 6401, 7032, 1497], 'generators': [3, 54, 648, 6, 972, 936, 1332], 'label': '1944.2466.3.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '1944.2466', 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '648.278'}
  • id: 107441220
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '9.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '216.92', 'aut_weyl_index': 18, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['18.v1.a1', '27.e1.a1', '27.f1.a1', '36.q1.a1'], 'core': '54.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1691, -1, 1124, -1, 7283, -1, 2618, -1], 'generators': [3, 972, 54, 722, 6, 648], 'label': '1944.2466.9.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '9.j1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.j1.a1', 'subgroup_fusion': None, 'weyl_group': '216.92'}
  • id: 107441221
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '9.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '216.92', 'aut_weyl_index': 18, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['18.v1.b1', '27.e1.b1', '27.f1.a1', '36.q1.b1'], 'core': '54.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [1691, -1, 925, -1, 7283, -1, 2802, -1], 'generators': [3, 972, 54, 1334, 6, 648], 'label': '1944.2466.9.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '9.j1.b1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.j1.b1', 'subgroup_fusion': None, 'weyl_group': '216.92'}
  • id: 107441222
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '9.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '108.26', 'aut_weyl_index': 36, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.a1'], 'contains': ['18.i1.a1', '18.m1.a1', '18.w1.a1', '27.e1.a1', '27.g1.a1'], 'core': '54.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2246, -1, 8591, -1, 6322, -1, 3401, -1], 'generators': [3, 648, 936, 972, 722, 54], 'label': '1944.2466.9.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '9.k1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.k1.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 107441223
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '9.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '108.26', 'aut_weyl_index': 36, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.a1'], 'contains': ['18.i1.b1', '18.m1.b1', '18.w1.b1', '27.e1.b1', '27.g1.a1'], 'core': '54.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [2246, -1, 9013, -1, 6322, -1, 3789, -1], 'generators': [3, 648, 936, 972, 1334, 54], 'label': '1944.2466.9.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '9.k1.b1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.k1.b1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 107441224
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '9.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '216.90', 'aut_weyl_index': 18, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.d1.a1'], 'contains': ['18.x1.a1', '27.e1.a1', '27.h1.a1', '36.s1.a1'], 'core': '54.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5295, -1, 2188, -1, 4037, -1, 9144, -1], 'generators': [3, 972, 54, 722, 1806, 648], 'label': '1944.2466.9.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '9.l1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.l1.a1', 'subgroup_fusion': None, 'weyl_group': '72.15'}
  • id: 107441225
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '9.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '216.90', 'aut_weyl_index': 18, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.d1.a1'], 'contains': ['18.x1.b1', '27.e1.b1', '27.h1.a1', '36.s1.b1'], 'core': '54.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5295, -1, 1334, -1, 4037, -1, 9341, -1], 'generators': [3, 972, 54, 1334, 1806, 648], 'label': '1944.2466.9.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '9.l1.b1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.l1.b1', 'subgroup_fusion': None, 'weyl_group': '72.15'}
  • id: 107441226
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '9.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '216.90', 'aut_weyl_index': 18, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.e1.a1'], 'contains': ['18.y1.a1', '27.e1.a1', '27.i1.a1', '36.t1.a1'], 'core': '54.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9875, -1, 3479, -1, 1123, -1, 6359, -1], 'generators': [3, 972, 54, 722, 906, 648], 'label': '1944.2466.9.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.e1.a1', 'old_label': '9.m1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.m1.a1', 'subgroup_fusion': None, 'weyl_group': '216.90'}
  • id: 107441227
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '9.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '216.90', 'aut_weyl_index': 18, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.e1.a1'], 'contains': ['18.y1.b1', '27.e1.b1', '27.i1.a1', '36.t1.b1'], 'core': '54.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9875, -1, 3374, -1, 1123, -1, 6674, -1], 'generators': [3, 972, 54, 1334, 906, 648], 'label': '1944.2466.9.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.e1.a1', 'old_label': '9.m1.b1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.m1.b1', 'subgroup_fusion': None, 'weyl_group': '216.90'}
  • id: 107441228
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '36.12', 'aut_weyl_index': 108, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.f1.a1', '6.g1.a1'], 'contains': ['24.a1.a1', '36.a1.a1', '36.b1.a1', '36.c1.a1', '36.d1.a1', '36.e1.a1', '36.f1.a1', '36.f1.b1', '36.g1.a1', '36.g1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4051, -1, 8138, -1, 5278, -1, 5327, -1], 'generators': [54, 648, 2, 936, 1332], 'label': '1944.2466.12.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '12.a1.a1', 'projective_image': '648.278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 107441229
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '108.25', 'aut_weyl_index': 36, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1', '4.a1.a1'], 'contains': ['24.b1.a1', '36.h1.a1', '36.i1.a1', '36.m1.a1', '36.q1.a1', '36.q1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4853, -1, 4515, -1, 3737, -1, 5609, -1], 'generators': [3, 648, 2, 1332, 6], 'label': '1944.2466.12.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '12.b1.a1', 'projective_image': '648.278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 107441230
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '432.535', 'aut_weyl_index': 9, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '9.a1.a1', '9.b1.a1', '9.f1.a1', '9.j1.a1', '9.j1.b1', '12.b1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2950, -1, 1551, -1, 6397, -1, 3354, -1], 'generators': [3, 54, 648, 2, 972, 1332, 6], 'label': '1944.2466.3.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': '648.278', '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': '216.92'}
  • id: 107441231
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '108.26', 'aut_weyl_index': 36, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '36.h1.a1', '36.j1.a1', '36.n1.a1', '36.r1.a1', '36.r1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5965, -1, 9732, -1, 2705, -1, 6551, -1], 'generators': [3, 648, 2, 1332, 936], 'label': '1944.2466.12.c1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '12.c1.a1', 'projective_image': '648.278', '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': '54.6'}
  • id: 107441232
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '108.26', 'aut_weyl_index': 36, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.d1.a1', '4.a1.a1'], 'contains': ['24.c1.a1', '36.h1.a1', '36.k1.a1', '36.o1.a1', '36.s1.a1', '36.s1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6506, -1, 5291, -1, 2273, -1, 9625, -1], 'generators': [3, 648, 2, 1332, 1806], 'label': '1944.2466.12.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '12.d1.a1', 'projective_image': '648.278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
  • id: 107441233
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '108.26', 'aut_weyl_index': 36, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.e1.a1', '4.a1.a1'], 'contains': ['24.d1.a1', '36.h1.a1', '36.l1.a1', '36.p1.a1', '36.t1.a1', '36.t1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9033, -1, 5926, -1, 578, -1, 7711, -1], 'generators': [3, 648, 2, 1332, 906], 'label': '1944.2466.12.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '12.e1.a1', 'projective_image': '648.278', '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': '54.6'}
  • id: 107441234
    {'ambient': '1944.2466', 'aut_centralizer_order': 2, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '486.177', 'aut_weyl_index': 8, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '4.a1.a1'], 'contains': ['24.e1.a1', '36.m1.a1', '36.n1.a1', '36.o1.a1', '36.p1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7044, -1, 6067, -1, 1869, -1, 7901, -1], 'generators': [3, 648, 6, 936, 1332], 'label': '1944.2466.12.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '1944.2466', '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': '162.20'}
  • id: 107441235
    {'ambient': '1944.2466', 'aut_centralizer_order': 108, 'aut_label': '18.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '36.13', 'aut_weyl_index': 108, 'centralizer': '18.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '6.d1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '54.a1.a1', '54.b1.a1', '54.c1.a1', '54.c1.b1', '54.n1.a1', '54.x1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5531, 2122, 2666, 7755, 6519, 2728, 3922, 7998], 'generators': [54, 648, 972, 2, 1332], 'label': '1944.2466.18.a1.a1', 'mobius_quo': 0, 'mobius_sub': -27, 'normal_closure': '18.a1.a1', 'normal_contained_in': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '6.d1.a1'], 'normal_contains': ['54.a1.a1', '54.c1.b1', '54.c1.a1', '54.b1.a1', '72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '648.278', 'quotient_action_image': '18.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107441236
    {'ambient': '1944.2466', 'aut_centralizer_order': 18, 'aut_label': '18.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '216.95', 'aut_weyl_index': 18, 'centralizer': '216.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.e1.a1', '6.h1.a1', '9.f1.a1'], 'contains': ['54.b1.a1', '54.p1.a1', '72.g1.a1'], 'core': '18.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7134, 3548, 2935, 4380, 4733, 4079, 5867, 1525], 'generators': [6, 972, 1332, 648, 54], 'label': '1944.2466.18.b1.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.b1.a1', 'normal_contained_in': ['6.a1.a1', '6.e1.a1'], 'normal_contains': ['54.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '1944.2466', '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': '216.95'}
  • id: 107441237
    {'ambient': '1944.2466', 'aut_centralizer_order': 72, 'aut_label': '18.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '54.8', 'aut_weyl_index': 72, 'centralizer': '54.a1.a1', 'complements': ['108.l1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.e1.a1', '6.i1.a1', '9.g1.a1'], 'contains': ['36.d1.a1', '54.b1.a1', '54.r1.a1'], 'core': '18.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6795, 8311, 5588, 1640, 4547, 7472, 6025, 4757], 'generators': [54, 648, 972, 936, 1332], 'label': '1944.2466.18.c1.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.c1.a1', 'normal_contained_in': ['6.b1.a1', '6.e1.a1'], 'normal_contains': ['54.b1.a1', '72.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.c1.a1', 'projective_image': '1944.2466', 'quotient_action_image': '6.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': '54.8'}
  • id: 107441238
    {'ambient': '1944.2466', 'aut_centralizer_order': 18, 'aut_label': '18.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '216.164', 'aut_weyl_index': 18, 'centralizer': '72.a1.a1', 'complements': ['108.l1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.e1.a1', '6.j1.a1', '9.h1.a1'], 'contains': ['54.b1.a1', '54.t1.a1', '72.j1.a1'], 'core': '18.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7302, 5143, 4078, 5954, 3389, 5591, 8654, 2965], 'generators': [1122, 972, 1332, 648, 54], 'label': '1944.2466.18.d1.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.d1.a1', 'normal_contained_in': ['6.c1.a1', '6.e1.a1'], 'normal_contains': ['54.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.d1.a1', 'projective_image': '1944.2466', 'quotient_action_image': '6.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '18.d1.a1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 107441239
    {'ambient': '1944.2466', 'aut_centralizer_order': 18, 'aut_label': '18.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '216.95', 'aut_weyl_index': 18, 'centralizer': '216.a1.a1', 'complements': ['108.l1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.e1.a1', '6.k1.a1', '9.i1.a1'], 'contains': ['54.b1.a1', '54.v1.a1', '72.l1.a1'], 'core': '18.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9284, 6727, 4252, 3203, 1308, 1376, 7249, 448], 'generators': [942, 972, 1332, 648, 54], 'label': '1944.2466.18.e1.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.e1.a1', 'normal_contained_in': ['6.d1.a1', '6.e1.a1'], 'normal_contains': ['54.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.e1.a1', 'projective_image': '1944.2466', 'quotient_action_image': '6.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '18.e1.a1', 'subgroup_fusion': None, 'weyl_group': '216.95'}
  • id: 107441240
    {'ambient': '1944.2466', '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.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.h1.a1', '54.d1.a1', '54.e1.a1', '54.f1.a1', '54.g1.a1', '54.g1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2363, -1, 3715, -1, 6292, -1, 3729, -1], 'generators': [3, 648, 54, 2, 1332], 'label': '1944.2466.18.f1.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': '18.f1.a1', 'projective_image': '648.278', '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: 107441241
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '3.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '216.111', 'aut_weyl_index': 18, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.a1', '6.f1.a1', '6.g1.a1', '9.a1.a1', '9.c1.a1', '9.g1.a1', '9.k1.a1', '9.k1.b1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3247, -1, 7778, -1, 6070, -1, 3789, -1], 'generators': [3, 936, 54, 972, 648, 2, 1332], 'label': '1944.2466.3.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '3.c1.a1', 'projective_image': '648.278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.c1.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 107441242
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '216.111', 'aut_weyl_index': 18, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '9.c1.a1'], 'contains': ['36.b1.a1', '36.j1.a1', '54.e1.a1', '54.h1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3216, -1, 9125, -1, 6078, -1, 4251, -1], 'generators': [3, 648, 54, 2, 936], 'label': '1944.2466.18.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.g1.a1', 'projective_image': '648.278', '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': '108.26'}
  • id: 107441243
    {'ambient': '1944.2466', 'aut_centralizer_order': 12, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '108.26', 'aut_weyl_index': 36, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '9.g1.a1'], 'contains': ['36.d1.a1', '36.n1.a1', '54.f1.a1', '54.h1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3556, -1, 8731, -1, 5685, -1, 4585, -1], 'generators': [3, 648, 54, 1332, 936], 'label': '1944.2466.18.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.h1.a1', 'projective_image': '1944.2466', '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': '108.26'}
  • id: 107441244
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '108.26', 'aut_weyl_index': 36, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '9.k1.a1'], 'contains': ['36.f1.a1', '36.r1.a1', '54.g1.a1', '54.h1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2870, -1, 9338, -1, 5890, -1, 4092, -1], 'generators': [3, 648, 54, 722, 936], 'label': '1944.2466.18.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.i1.a1', 'projective_image': '1944.2466', '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': '108.26'}
  • id: 107441245
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '108.26', 'aut_weyl_index': 36, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '9.k1.b1'], 'contains': ['36.f1.b1', '36.r1.b1', '54.g1.b1', '54.h1.a1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [2870, -1, 9531, -1, 5890, -1, 4410, -1], 'generators': [3, 648, 54, 1334, 936], 'label': '1944.2466.18.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.i1.b1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.i1.b1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 107441246
    {'ambient': '1944.2466', 'aut_centralizer_order': 18, 'aut_label': '18.j1', '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.g1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '54.i1.a1', '54.j1.a1', '54.k1.a1', '54.l1.a1', '54.l1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1275, -1, 3531, -1, 8055, -1, 2094, -1], 'generators': [975, 648, 2, 1332, 54], 'label': '1944.2466.18.j1.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': '18.j1.a1', 'projective_image': '648.278', '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': '12.4'}
  • id: 107441247
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '18.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '216.111', 'aut_weyl_index': 18, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '9.c1.a1'], 'contains': ['36.b1.a1', '54.i1.a1', '54.m1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2111, -1, 7673, -1, 7836, -1, 2405, -1], 'generators': [975, 648, 2, 54, 936], 'label': '1944.2466.18.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.k1.a1', 'projective_image': '648.278', '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': '108.26'}
  • id: 107441248
    {'ambient': '1944.2466', 'aut_centralizer_order': 12, 'aut_label': '18.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '108.26', 'aut_weyl_index': 36, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '9.g1.a1'], 'contains': ['36.d1.a1', '54.k1.a1', '54.m1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3029, -1, 6358, -1, 7055, -1, 3284, -1], 'generators': [975, 648, 1332, 54, 936], 'label': '1944.2466.18.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.l1.a1', 'projective_image': '1944.2466', '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': '108.26'}
  • id: 107441249
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '18.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '108.26', 'aut_weyl_index': 36, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '9.k1.a1'], 'contains': ['36.f1.a1', '54.l1.a1', '54.m1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1781, -1, 8317, -1, 7454, -1, 2255, -1], 'generators': [975, 648, 722, 54, 936], 'label': '1944.2466.18.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.m1.a1', 'projective_image': '1944.2466', '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': '108.26'}
  • id: 107441250
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '18.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '108.26', 'aut_weyl_index': 36, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '9.k1.b1'], 'contains': ['36.f1.b1', '54.l1.b1', '54.m1.a1'], 'core': '216.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [1781, -1, 8970, -1, 7454, -1, 2905, -1], 'generators': [975, 648, 1334, 54, 936], 'label': '1944.2466.18.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.m1.b1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.m1.b1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 107441251
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '18.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.188', 'aut_weyl_index': 27, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '9.b1.a1'], 'contains': ['54.a1.a1', '54.o1.a1', '54.p1.a1', '54.q1.a1', '54.y1.a1', '72.c1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1478, -1, 535, -1, 9243, -1, 612, -1], 'generators': [2, 972, 6, 648, 54], 'label': '1944.2466.18.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.n1.a1', 'projective_image': '648.278', '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': '72.42'}
  • id: 107441252
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '3.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '432.533', 'aut_weyl_index': 9, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.c1.a1', '9.a1.a1', '9.d1.a1', '9.h1.a1', '9.l1.a1', '9.l1.b1', '12.d1.a1'], 'core': '6.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5667, -1, 2335, -1, 3696, -1, 8848, -1], 'generators': [3, 54, 648, 2, 972, 1332, 1806], 'label': '1944.2466.3.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '3.d1.a1', 'projective_image': '648.278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.d1.a1', 'subgroup_fusion': None, 'weyl_group': '72.15'}
  • id: 107441253
    {'ambient': '1944.2466', 'aut_centralizer_order': 108, 'aut_label': '18.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.5', 'aut_weyl_index': 324, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '9.c1.a1'], 'contains': ['36.b1.a1', '36.c1.a1', '54.a1.a1', '54.r1.a1', '54.s1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4700, -1, 7519, -1, 5481, -1, 4956, -1], 'generators': [54, 648, 972, 2, 936], 'label': '1944.2466.18.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.o1.a1', 'projective_image': '648.278', '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': '6.2'}
  • id: 107441254
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.188', 'aut_weyl_index': 27, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '9.d1.a1'], 'contains': ['54.a1.a1', '54.t1.a1', '54.u1.a1', '72.e1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6416, -1, 1757, -1, 4316, -1, 8891, -1], 'generators': [2, 972, 1122, 648, 54], 'label': '1944.2466.18.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '18.p1.a1', 'projective_image': '648.278', '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': '24.12'}
  • id: 107441255
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '18.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.188', 'aut_weyl_index': 27, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '9.e1.a1'], 'contains': ['54.a1.a1', '54.v1.a1', '54.w1.a1', '72.f1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9665, -1, 2400, -1, 798, -1, 6895, -1], 'generators': [2, 972, 942, 648, 54], 'label': '1944.2466.18.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.e1.a1', 'old_label': '18.q1.a1', 'projective_image': '648.278', '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': '72.42'}
  • id: 107441256
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '18.r1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '216.95', 'aut_weyl_index': 18, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.i1.a1', '6.j1.a1', '6.k1.a1'], 'contains': ['54.b1.a1', '54.q1.a1', '72.h1.a1'], 'core': '54.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8020, -1, 4357, -1, 2878, -1, 7564, -1], 'generators': [8, 972, 1332, 648, 54], 'label': '1944.2466.18.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '18.r1.a1', 'projective_image': '1944.2466', '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': '108.22'}
  • id: 107441257
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '18.s1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '54.8', 'aut_weyl_index': 72, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.h1.a1', '6.j1.a1', '6.k1.a1'], 'contains': ['36.e1.a1', '54.b1.a1', '54.s1.a1'], 'core': '54.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8189, -1, 5096, -1, 3157, -1, 6365, -1], 'generators': [54, 648, 972, 938, 1332], 'label': '1944.2466.18.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '18.s1.a1', 'projective_image': '1944.2466', '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': '27.3'}
  • id: 107441258
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '18.t1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '216.164', 'aut_weyl_index': 18, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.h1.a1', '6.i1.a1', '6.k1.a1'], 'contains': ['54.b1.a1', '54.u1.a1', '72.k1.a1'], 'core': '54.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7681, -1, 4781, -1, 2486, -1, 8418, -1], 'generators': [950, 972, 1332, 648, 54], 'label': '1944.2466.18.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '18.t1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.t1.a1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 107441259
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '18.u1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '216.95', 'aut_weyl_index': 18, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.h1.a1', '6.i1.a1', '6.j1.a1'], 'contains': ['54.b1.a1', '54.w1.a1', '72.m1.a1'], 'core': '54.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8697, -1, 4956, -1, 2013, -1, 7406, -1], 'generators': [944, 972, 1332, 648, 54], 'label': '1944.2466.18.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '18.u1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.u1.a1', 'subgroup_fusion': None, 'weyl_group': '108.22'}
  • id: 107441260
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '18.v1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.42', 'aut_weyl_index': 54, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '9.j1.a1'], 'contains': ['54.c1.a1', '54.p1.a1', '54.q1.a1', '72.n1.a1'], 'core': '54.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2629, -1, 982, -1, 8436, -1, 1652, -1], 'generators': [722, 972, 6, 648, 54], 'label': '1944.2466.18.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.v1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.v1.a1', 'subgroup_fusion': None, 'weyl_group': '72.42'}
  • id: 107441261
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '18.v1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.42', 'aut_weyl_index': 54, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '9.j1.b1'], 'contains': ['54.c1.b1', '54.p1.a1', '54.q1.a1', '72.n1.b1'], 'core': '54.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [2629, -1, 877, -1, 8436, -1, 1770, -1], 'generators': [1334, 972, 6, 648, 54], 'label': '1944.2466.18.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.v1.b1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.v1.b1', 'subgroup_fusion': None, 'weyl_group': '72.42'}
  • id: 107441262
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '18.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '18.3', 'aut_weyl_index': 216, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '9.k1.a1'], 'contains': ['36.f1.a1', '36.g1.a1', '54.c1.a1', '54.r1.a1', '54.s1.a1'], 'core': '54.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4503, -1, 7963, -1, 5059, -1, 4771, -1], 'generators': [54, 648, 972, 722, 936], 'label': '1944.2466.18.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.w1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.w1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 107441263
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '3.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '432.533', 'aut_weyl_index': 9, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.d1.a1', '9.a1.a1', '9.e1.a1', '9.i1.a1', '9.m1.a1', '9.m1.b1', '12.e1.a1'], 'core': '6.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9116, -1, 3670, -1, 1308, -1, 6732, -1], 'generators': [3, 54, 648, 2, 972, 1332, 906], 'label': '1944.2466.3.e1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.e1.a1', 'old_label': '3.e1.a1', 'projective_image': '648.278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.e1.a1', 'subgroup_fusion': None, 'weyl_group': '216.90'}
  • id: 107441264
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '18.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '18.3', 'aut_weyl_index': 216, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '9.k1.b1'], 'contains': ['36.f1.b1', '36.g1.b1', '54.c1.b1', '54.r1.a1', '54.s1.a1'], 'core': '54.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [4503, -1, 8496, -1, 5059, -1, 5140, -1], 'generators': [54, 648, 972, 1334, 936], 'label': '1944.2466.18.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.w1.b1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.w1.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 107441265
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '18.x1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.42', 'aut_weyl_index': 54, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '9.l1.a1'], 'contains': ['54.c1.a1', '54.t1.a1', '54.u1.a1', '72.p1.a1'], 'core': '54.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6078, -1, 1932, -1, 4037, -1, 9088, -1], 'generators': [722, 972, 1122, 648, 54], 'label': '1944.2466.18.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '18.x1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.x1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107441266
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '18.x1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.42', 'aut_weyl_index': 54, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '9.l1.b1'], 'contains': ['54.c1.b1', '54.t1.a1', '54.u1.a1', '72.p1.b1'], 'core': '54.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6078, -1, 1582, -1, 4037, -1, 9285, -1], 'generators': [1334, 972, 1122, 648, 54], 'label': '1944.2466.18.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '18.x1.b1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.x1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 107441267
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '18.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.42', 'aut_weyl_index': 54, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '9.m1.a1'], 'contains': ['54.c1.a1', '54.v1.a1', '54.w1.a1', '72.q1.a1'], 'core': '54.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9874, -1, 3391, -1, 1123, -1, 6698, -1], 'generators': [722, 972, 942, 648, 54], 'label': '1944.2466.18.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.e1.a1', 'old_label': '18.y1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.y1.a1', 'subgroup_fusion': None, 'weyl_group': '72.42'}
  • id: 107441268
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '18.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.42', 'aut_weyl_index': 54, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '9.m1.b1'], 'contains': ['54.c1.b1', '54.v1.a1', '54.w1.a1', '72.q1.b1'], 'core': '54.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9874, -1, 3287, -1, 1123, -1, 7052, -1], 'generators': [1334, 972, 942, 648, 54], 'label': '1944.2466.18.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.e1.a1', 'old_label': '18.y1.b1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.y1.b1', 'subgroup_fusion': None, 'weyl_group': '72.42'}
  • id: 107441269
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '108.28', 'aut_weyl_index': 36, 'centralizer': '54.a1.a1', 'complements': ['81.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.c1.a1'], 'contains': ['72.a1.a1', '72.b1.a1', '72.d1.a1', '72.i1.a1', '72.o1.a1', '72.o1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6426, 9102, 9495, 776, 2336, 9254, 6827, 6454], 'generators': [2, 936, 1332], 'label': '1944.2466.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['6.b1.a1'], 'normal_contains': ['72.a1.a1', '72.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '648.278', 'quotient_action_image': '6.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '54.8'}
  • id: 107441270
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '108.28', 'aut_weyl_index': 36, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '8.a1.a1', '12.b1.a1'], 'contains': ['72.a1.a1', '72.c1.a1', '72.g1.a1', '72.h1.a1', '72.n1.a1', '72.n1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5165, -1, 4784, -1, 2888, -1, 6368, -1], 'generators': [2, 6, 1332], 'label': '1944.2466.24.b1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '648.278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '54.8'}
  • id: 107441271
    {'ambient': '1944.2466', 'aut_centralizer_order': 27, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.12', 'aut_weyl_index': 108, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '8.a1.a1', '12.d1.a1'], 'contains': ['72.a1.a1', '72.e1.a1', '72.j1.a1', '72.k1.a1', '72.p1.a1', '72.p1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7372, -1, 5690, -1, 1920, -1, 8954, -1], 'generators': [2, 1122, 1332], 'label': '1944.2466.24.c1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '648.278', '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: 107441272
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '108.28', 'aut_weyl_index': 36, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '8.a1.a1', '12.e1.a1'], 'contains': ['72.a1.a1', '72.f1.a1', '72.l1.a1', '72.m1.a1', '72.q1.a1', '72.q1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9175, -1, 6309, -1, 514, -1, 8094, -1], 'generators': [2, 942, 1332], 'label': '1944.2466.24.d1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '648.278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '54.8'}
  • id: 107441273
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '162.41', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '8.a1.a1', '12.f1.a1'], 'contains': ['72.b1.a1', '72.g1.a1', '72.j1.a1', '72.l1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7850, -1, 6611, -1, 1667, -1, 8421, -1], 'generators': [6, 936], 'label': '1944.2466.24.e1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '24.e1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '54.8'}
  • id: 107441274
    {'ambient': '1944.2466', 'aut_centralizer_order': 1, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '972.678', 'aut_weyl_index': 4, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.a1.a1', '12.b1.a1', '12.c1.a1', '12.d1.a1', '12.e1.a1', '12.f1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7044, -1, 6282, -1, 2273, -1, 7829, -1], 'generators': [3, 648, 1332, 2, 6, 936], 'label': '1944.2466.4.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '648.278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '162.20'}
  • id: 107441275
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '162.41', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '8.a1.a1'], 'contains': ['72.g1.a1', '72.i1.a1', '72.k1.a1', '72.m1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8421, -1, 7215, -1, 1418, -1, 8274, -1], 'generators': [938, 6], 'label': '1944.2466.24.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '24.f1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 107441276
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '162.41', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '8.a1.a1'], 'contains': ['72.b1.a1', '72.h1.a1', '72.k1.a1', '72.m1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8308, -1, 7542, -1, 1293, -1, 8527, -1], 'generators': [8, 936], 'label': '1944.2466.24.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '24.g1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 107441277
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '162.41', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.a1', '8.a1.a1'], 'contains': ['72.h1.a1', '72.i1.a1', '72.j1.a1', '72.m1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8667, -1, 7035, -1, 1542, -1, 8738, -1], 'generators': [938, 1122], 'label': '1944.2466.24.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '24.h1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.a1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 107441278
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '162.41', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1.a1', '8.a1.a1'], 'contains': ['72.h1.a1', '72.i1.a1', '72.k1.a1', '72.l1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8851, -1, 6916, -1, 1121, -1, 8633, -1], 'generators': [938, 942], 'label': '1944.2466.24.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '24.i1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.a1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 107441279
    {'ambient': '1944.2466', 'aut_centralizer_order': 18, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.5', 'aut_weyl_index': 486, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1'], 'contains': ['54.d1.a1', '54.j1.a1', '54.n1.a1', '81.a1.a1', '81.b1.a1', '81.c1.a1', '81.c1.b1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [724, -1, 749, -1, 8268, -1, 1913, -1], 'generators': [3, 54, 972, 2, 36], 'label': '1944.2466.27.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': '648.278', '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': '4.2'}
  • id: 107441280
    {'ambient': '1944.2466', 'aut_centralizer_order': 18, 'aut_label': '27.b1', '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': ['9.a1.a1', '9.b1.a1', '9.c1.a1', '9.d1.a1', '9.e1.a1'], 'contains': ['54.a1.a1', '54.e1.a1', '54.i1.a1', '81.a1.a1', '81.d1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2211, -1, 1360, -1, 7630, -1, 2580, -1], 'generators': [3, 648, 972, 2, 54], 'label': '1944.2466.27.b1.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': '27.b1.a1', 'projective_image': '648.278', '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': '12.4'}
  • id: 107441281
    {'ambient': '1944.2466', 'aut_centralizer_order': 3, 'aut_label': '27.c1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '48.48', 'aut_weyl_index': 81, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1.a1'], 'contains': ['54.o1.a1', '81.a1.a1', '81.e1.a1', '108.l1.a1'], 'core': '162.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [118, -1, 182, -1, 9839, -1, 370, -1], 'generators': [3, 972, 2, 6, 54], 'label': '1944.2466.27.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': '648.278', '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': '24.12'}
  • id: 107441282
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '27.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '9.f1.a1', '9.g1.a1', '9.h1.a1', '9.i1.a1'], 'contains': ['54.b1.a1', '54.f1.a1', '54.k1.a1', '81.b1.a1', '81.d1.a1'], 'core': '54.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3679, -1, 3098, -1, 6718, -1, 3531, -1], 'generators': [3, 648, 972, 1332, 54], 'label': '1944.2466.27.d1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '27.d1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107441283
    {'ambient': '1944.2466', 'aut_centralizer_order': 18, 'aut_label': '27.e1', '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': ['9.a1.a1', '9.j1.a1', '9.k1.a1', '9.l1.a1', '9.m1.a1'], 'contains': ['54.c1.a1', '54.g1.a1', '54.l1.a1', '81.c1.a1', '81.d1.a1'], 'core': '54.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1856, -1, 2305, -1, 7278, -1, 2755, -1], 'generators': [3, 648, 972, 722, 54], 'label': '1944.2466.27.e1.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': '27.e1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107441284
    {'ambient': '1944.2466', 'aut_centralizer_order': 18, 'aut_label': '27.e1', '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': ['9.a1.a1', '9.j1.b1', '9.k1.b1', '9.l1.b1', '9.m1.b1'], 'contains': ['54.c1.b1', '54.g1.b1', '54.l1.b1', '81.c1.b1', '81.d1.a1'], 'core': '54.c1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [1856, -1, 2115, -1, 7278, -1, 3094, -1], 'generators': [3, 648, 972, 1334, 54], 'label': '1944.2466.27.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '27.e1.b1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.e1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107441285
    {'ambient': '1944.2466', 'aut_centralizer_order': 9, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '432.538', 'aut_weyl_index': 9, 'centralizer': '216.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.a1'], 'contains': ['18.a1.a1', '18.b1.a1', '18.n1.a1', '18.r1.a1', '18.v1.a1', '18.v1.b1', '24.b1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5134, 898, 2074, 6777, 5612, 2728, 3994, 3947], 'generators': [2, 972, 54, 6, 1332, 648], 'label': '1944.2466.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['18.a1.a1', '18.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '648.278', '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': '216.95'}
  • id: 107441286
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '27.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '216.92', 'aut_weyl_index': 18, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1.a1', '9.f1.a1', '9.j1.a1', '9.j1.b1'], 'contains': ['54.p1.a1', '81.d1.a1', '81.e1.a1', '108.o1.a1'], 'core': '162.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [917, -1, 323, -1, 9396, -1, 1545, -1], 'generators': [3, 972, 6, 648, 54], 'label': '1944.2466.27.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '27.f1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.f1.a1', 'subgroup_fusion': None, 'weyl_group': '216.92'}
  • id: 107441287
    {'ambient': '1944.2466', 'aut_centralizer_order': 12, 'aut_label': '27.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '108.26', 'aut_weyl_index': 36, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1.a1', '9.g1.a1', '9.k1.a1', '9.k1.b1'], 'contains': ['54.h1.a1', '54.m1.a1', '54.r1.a1', '81.d1.a1'], 'core': '162.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2771, -1, 8864, -1, 6924, -1, 3395, -1], 'generators': [3, 648, 972, 54, 936], 'label': '1944.2466.27.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '27.g1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.g1.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 107441288
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '27.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '216.90', 'aut_weyl_index': 18, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.d1.a1', '9.h1.a1', '9.l1.a1', '9.l1.b1'], 'contains': ['54.t1.a1', '81.d1.a1', '108.q1.a1'], 'core': '162.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5379, -1, 1194, -1, 4873, -1, 9483, -1], 'generators': [3, 972, 1806, 648, 54], 'label': '1944.2466.27.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '27.h1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.h1.a1', 'subgroup_fusion': None, 'weyl_group': '72.15'}
  • id: 107441289
    {'ambient': '1944.2466', 'aut_centralizer_order': 6, 'aut_label': '27.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '216.90', 'aut_weyl_index': 18, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.e1.a1', '9.i1.a1', '9.m1.a1', '9.m1.b1'], 'contains': ['54.v1.a1', '81.d1.a1', '108.r1.a1'], 'core': '162.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9970, -1, 2791, -1, 984, -1, 6207, -1], 'generators': [3, 972, 906, 648, 54], 'label': '1944.2466.27.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.e1.a1', 'old_label': '27.i1.a1', 'projective_image': '1944.2466', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.i1.a1', 'subgroup_fusion': None, 'weyl_group': '216.90'}
  • id: 107441290
    {'ambient': '1944.2466', 'aut_centralizer_order': 108, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 324, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.a1.a1', '18.f1.a1', '18.j1.a1'], 'contains': ['72.a1.a1', '108.a1.a1', '108.b1.a1', '108.c1.a1', '108.d1.a1', '108.d1.b1', '108.i1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2461, -1, 4428, -1, 6896, -1, 3353, -1], 'generators': [54, 2, 1332, 648], 'label': '1944.2466.36.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.a1.a1', 'projective_image': '648.278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107441291
    {'ambient': '1944.2466', 'aut_centralizer_order': 108, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.5', 'aut_weyl_index': 324, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.g1.a1', '18.k1.a1', '18.o1.a1'], 'contains': ['72.d1.a1', '108.a1.a1', '108.e1.a1', '108.g1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3619, -1, 7974, -1, 6154, -1, 4245, -1], 'generators': [54, 2, 936, 648], 'label': '1944.2466.36.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.b1.a1', 'projective_image': '648.278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 107441292
    {'ambient': '1944.2466', 'aut_centralizer_order': 108, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 648, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.o1.a1'], 'contains': ['72.d1.a1', '108.a1.a1', '108.f1.a1', '108.h1.a1', '108.h1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4301, -1, 8125, -1, 5135, -1, 5493, -1], 'generators': [972, 2, 936, 648], 'label': '1944.2466.36.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '36.c1.a1', 'projective_image': '648.278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 107441293
    {'ambient': '1944.2466', 'aut_centralizer_order': 72, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '18.3', 'aut_weyl_index': 216, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.c1.a1', '18.h1.a1', '18.l1.a1'], 'contains': ['72.b1.a1', '108.c1.a1', '108.e1.a1', '108.f1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3931, -1, 7820, -1, 5539, -1, 4975, -1], 'generators': [54, 936, 1332, 648], 'label': '1944.2466.36.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.d1.a1', 'projective_image': '1944.2466', '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': '18.3'}
  • id: 107441294
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '18.3', 'aut_weyl_index': 216, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.s1.a1'], 'contains': ['72.i1.a1', '108.c1.a1', '108.g1.a1', '108.h1.a1', '108.h1.b1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6601, -1, 7206, -1, 4726, -1, 5841, -1], 'generators': [54, 938, 1332, 648], 'label': '1944.2466.36.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '36.e1.a1', 'projective_image': '1944.2466', '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': '9.2'}
  • id: 107441295
    {'ambient': '1944.2466', 'aut_centralizer_order': 36, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '18.3', 'aut_weyl_index': 216, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.i1.a1', '18.m1.a1', '18.w1.a1'], 'contains': ['72.o1.a1', '108.d1.a1', '108.e1.a1', '108.h1.b1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3435, -1, 8716, -1, 5951, -1, 4072, -1], 'generators': [54, 722, 936, 648], 'label': '1944.2466.36.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.f1.a1', 'projective_image': '1944.2466', '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': '18.3'}