Abstract group data - 1152.155799

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [6, 2, 3, 4, 2, 12, 2, 3, 12, 2, 2], 'aut_gens': [[1, 2, 4, 96, 192], [433, 162, 100, 672, 864], [1, 2, 52, 96, 960], [1, 66, 4, 672, 864], [817, 82, 164, 96, 1056], [1, 578, 580, 96, 192], [769, 626, 620, 672, 192], [1, 578, 676, 96, 192], [385, 2, 4, 96, 192], [385, 730, 716, 96, 288], [49, 2, 20, 672, 192], [1, 2, 20, 672, 960]], 'aut_group': '4608.lj', 'aut_hash': 3301011005301566777, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 4608, 'aut_permdeg': 34, 'aut_perms': [87514120271643561366612314978048848096, 8131621669012344578998917140011620511, 1782791949799304055349332858506729105, 160240953049776699860811498955555419993, 3733717570564882422228212331256084069, 119147756350193604850190826401052139875, 3699765204928364195280260942231274086, 43688262534802629759982882269978624000, 49467354214418156760197113572781329281, 42810753092240988596389347172082411862, 8077509762945163510312110687249131862], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 3, 2, 1], [2, 9, 2, 1], [2, 24, 1, 1], [2, 72, 1, 1], [3, 2, 1, 1], [3, 8, 1, 1], [3, 16, 1, 1], [4, 2, 1, 1], [4, 6, 1, 2], [4, 18, 1, 1], [4, 24, 1, 3], [4, 72, 1, 3], [6, 2, 1, 1], [6, 6, 1, 2], [6, 8, 1, 1], [6, 16, 1, 1], [6, 24, 2, 1], [6, 48, 1, 1], [8, 2, 2, 1], [8, 6, 2, 2], [8, 18, 2, 1], [12, 4, 1, 1], [12, 8, 2, 1], [12, 12, 1, 1], [12, 16, 2, 1], [12, 24, 2, 1], [12, 48, 1, 3], [24, 4, 2, 1], [24, 8, 4, 1], [24, 12, 2, 1], [24, 16, 4, 1], [24, 24, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^5.D_6^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '576.8659', 'autcentquo_hash': 8659, 'autcentquo_nilpotent': False, 'autcentquo_order': 576, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2^2:D_6^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 4], [2, 9, 2], [2, 24, 1], [2, 72, 1], [3, 2, 1], [3, 8, 1], [3, 16, 1], [4, 2, 1], [4, 6, 2], [4, 18, 1], [4, 24, 3], [4, 72, 3], [6, 2, 1], [6, 6, 2], [6, 8, 1], [6, 16, 1], [6, 24, 2], [6, 48, 1], [8, 2, 2], [8, 6, 4], [8, 18, 2], [12, 4, 1], [12, 8, 2], [12, 12, 1], [12, 16, 2], [12, 24, 2], [12, 48, 3], [24, 4, 2], [24, 8, 4], [24, 12, 2], [24, 16, 4], [24, 24, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '576.8312', 'commutator_count': 1, 'commutator_label': '144.155', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 155799, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['192.960', 1], ['6.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 4], [2, 9, 1, 2], [2, 24, 1, 1], [2, 72, 1, 1], [3, 2, 1, 1], [3, 8, 1, 1], [3, 16, 1, 1], [4, 2, 1, 1], [4, 6, 1, 2], [4, 18, 1, 1], [4, 24, 1, 3], [4, 72, 1, 3], [6, 2, 1, 1], [6, 6, 1, 2], [6, 8, 1, 1], [6, 16, 1, 1], [6, 24, 1, 2], [6, 48, 1, 1], [8, 2, 2, 1], [8, 6, 2, 2], [8, 18, 2, 1], [12, 4, 1, 1], [12, 8, 2, 1], [12, 12, 1, 1], [12, 16, 2, 1], [12, 24, 2, 1], [12, 48, 1, 3], [24, 4, 2, 1], [24, 8, 4, 1], [24, 12, 2, 1], [24, 16, 4, 1], [24, 24, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 80640, 'exponent': 24, 'exponents_of_order': [7, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 2]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '288.1028', 'hash': 155799, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 2, 12, 2, 6], 'inner_gens': [[1, 2, 4, 96, 960], [1, 2, 44, 672, 192], [1, 58, 4, 576, 288], [1, 578, 676, 96, 192], [385, 2, 100, 96, 192]], 'inner_hash': 8312, 'inner_nilpotent': False, 'inner_order': 576, 'inner_split': True, 'inner_tex': 'S_3\\times C_4:S_4', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': 12, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 8], [2, 26], [3, 8], [4, 11], [6, 10], [12, 3]], 'label': '1152.155799', 'linC_count': 432, 'linC_degree': 7, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 9, 'linQ_degree_count': 64, 'linQ_dim': 9, 'linQ_dim_count': 64, 'linR_count': 192, 'linR_degree': 9, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'S3*C8:S4', 'ngens': 9, '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': 45, 'number_characteristic_subgroups': 53, 'number_conjugacy_classes': 66, 'number_divisions': 48, 'number_normal_subgroups': 59, 'number_subgroup_autclasses': 580, 'number_subgroup_classes': 622, 'number_subgroups': 6166, 'old_label': None, 'order': 1152, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 127], [3, 26], [4, 320], [6, 134], [8, 64], [12, 256], [24, 224]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[1, 2, 20, 672, 960], [49, 2, 4, 96, 960], [1, 2, 68, 672, 192]], 'outer_group': '8.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [1, 6, 120], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 10], [3, 8], [4, 7], [6, 6], [8, 4], [12, 3], [16, 1], [24, 1]], 'representations': {'PC': {'code': '1150496656393967828612400497347100368193579641488105606561359875480303625', 'gens': [1, 2, 3, 7, 8], 'pres': [9, -2, -2, -2, -2, -2, -3, -2, 2, -3, 605, 74, 1596, 102, 1813, 130, 1742, 21183, 9096, 5325, 2310, 1374, 69127, 5209, 7810, 1339, 1996, 214, 62216]}, 'Perm': {'d': 15, 'gens': [88216168440, 2047006085, 194123422080, 288409806720, 88216168320, 3, 840, 7, 16]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'S_3\\times C_8:S_4', 'transitive_degree': 72, '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: 108500321
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 155799, 'group_order': 1152, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 108500332
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 155799, 'group_order': 1152, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 48, 'size': 1}
  • id: 108500343
    {'aut_label': '2B', 'centralizer': '3.a1.a1', 'counter': 3, 'group_counter': 155799, 'group_order': 1152, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 1, 'size': 3}
  • id: 108500354
    {'aut_label': '2B', 'centralizer': '3.a1.a1', 'counter': 4, 'group_counter': 155799, 'group_order': 1152, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 49, 'size': 3}
  • id: 108500365
    {'aut_label': '2D', 'centralizer': '3.b1.a1', 'counter': 5, 'group_counter': 155799, 'group_order': 1152, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 672, 'size': 3}
  • id: 108500376
    {'aut_label': '2E', 'centralizer': '3.b1.a1', 'counter': 6, 'group_counter': 155799, 'group_order': 1152, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 624, 'size': 3}
  • id: 108500384
    {'aut_label': '2F', 'centralizer': '9.a1.a1', 'counter': 7, 'group_counter': 155799, 'group_order': 1152, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 193, 'size': 9}
  • id: 108500385
    {'aut_label': '2F', 'centralizer': '9.a1.a1', 'counter': 8, 'group_counter': 155799, 'group_order': 1152, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 241, 'size': 9}
  • id: 108500386
    {'aut_label': '2H', 'centralizer': '24.j1.a1', 'counter': 9, 'group_counter': 155799, 'group_order': 1152, 'label': '2H', 'order': 2, 'powers': [1, 9], 'representative': 18, 'size': 24}
  • id: 108500322
    {'aut_label': '2I', 'centralizer': '72.b1.a1', 'counter': 10, 'group_counter': 155799, 'group_order': 1152, 'label': '2I', 'order': 2, 'powers': [1, 10], 'representative': 139, 'size': 72}
  • id: 108500323
    {'aut_label': '3A', 'centralizer': '2.d1.a1', 'counter': 11, 'group_counter': 155799, 'group_order': 1152, 'label': '3A', 'order': 3, 'powers': [11, 1], 'representative': 768, 'size': 2}
  • id: 108500324
    {'aut_label': '3B', 'centralizer': '8.f1.a1', 'counter': 12, 'group_counter': 155799, 'group_order': 1152, 'label': '3B', 'order': 3, 'powers': [12, 1], 'representative': 64, 'size': 8}
  • id: 108500325
    {'aut_label': '3C', 'centralizer': '16.k1.a1', 'counter': 13, 'group_counter': 155799, 'group_order': 1152, 'label': '3C', 'order': 3, 'powers': [13, 1], 'representative': 800, 'size': 16}
  • id: 108500326
    {'aut_label': '4A', 'centralizer': '2.c1.a1', 'counter': 14, 'group_counter': 155799, 'group_order': 1152, 'label': '4A', 'order': 4, 'powers': [2, 14], 'representative': 72, 'size': 2}
  • id: 108500327
    {'aut_label': '4B', 'centralizer': '6.a1.a1', 'counter': 15, 'group_counter': 155799, 'group_order': 1152, 'label': '4B', 'order': 4, 'powers': [2, 15], 'representative': 648, 'size': 6}
  • id: 108500328
    {'aut_label': '4C', 'centralizer': '6.e1.a1', 'counter': 16, 'group_counter': 155799, 'group_order': 1152, 'label': '4C', 'order': 4, 'powers': [2, 16], 'representative': 25, 'size': 6}
  • id: 108500329
    {'aut_label': '4D', 'centralizer': '18.g1.a1', 'counter': 17, 'group_counter': 155799, 'group_order': 1152, 'label': '4D', 'order': 4, 'powers': [2, 17], 'representative': 217, 'size': 18}
  • id: 108500330
    {'aut_label': '4E', 'centralizer': '24.m1.a1', 'counter': 18, 'group_counter': 155799, 'group_order': 1152, 'label': '4E', 'order': 4, 'powers': [5, 18], 'representative': 610, 'size': 24}
  • id: 108500331
    {'aut_label': '4F', 'centralizer': '24.n1.a1', 'counter': 19, 'group_counter': 155799, 'group_order': 1152, 'label': '4F', 'order': 4, 'powers': [2, 19], 'representative': 94, 'size': 24}
  • id: 108500333
    {'aut_label': '4G', 'centralizer': '24.o1.a1', 'counter': 20, 'group_counter': 155799, 'group_order': 1152, 'label': '4G', 'order': 4, 'powers': [6, 20], 'representative': 734, 'size': 24}
  • id: 108500334
    {'aut_label': '4H', 'centralizer': '72.g1.a1', 'counter': 21, 'group_counter': 155799, 'group_order': 1152, 'label': '4H', 'order': 4, 'powers': [6, 21], 'representative': 303, 'size': 72}
  • id: 108500335
    {'aut_label': '4I', 'centralizer': '72.e1.a1', 'counter': 22, 'group_counter': 155799, 'group_order': 1152, 'label': '4I', 'order': 4, 'powers': [5, 22], 'representative': 947, 'size': 72}
  • id: 108500336
    {'aut_label': '4J', 'centralizer': '72.f1.a1', 'counter': 23, 'group_counter': 155799, 'group_order': 1152, 'label': '4J', 'order': 4, 'powers': [2, 23], 'representative': 311, 'size': 72}
  • id: 108500337
    {'aut_label': '6A', 'centralizer': '2.d1.a1', 'counter': 24, 'group_counter': 155799, 'group_order': 1152, 'label': '6A', 'order': 6, 'powers': [11, 2], 'representative': 432, 'size': 2}
  • id: 108500338
    {'aut_label': '6B', 'centralizer': '6.p1.a1', 'counter': 25, 'group_counter': 155799, 'group_order': 1152, 'label': '6B', 'order': 6, 'powers': [11, 5], 'representative': 288, 'size': 6}
  • id: 108500339
    {'aut_label': '6C', 'centralizer': '6.p1.a1', 'counter': 26, 'group_counter': 155799, 'group_order': 1152, 'label': '6C', 'order': 6, 'powers': [11, 6], 'representative': 1008, 'size': 6}
  • id: 108500340
    {'aut_label': '6D', 'centralizer': '8.f1.a1', 'counter': 27, 'group_counter': 155799, 'group_order': 1152, 'label': '6D', 'order': 6, 'powers': [12, 2], 'representative': 16, 'size': 8}
  • id: 108500341
    {'aut_label': '6E', 'centralizer': '16.k1.a1', 'counter': 28, 'group_counter': 155799, 'group_order': 1152, 'label': '6E', 'order': 6, 'powers': [13, 2], 'representative': 400, 'size': 16}
  • id: 108500342
    {'aut_label': '6F', 'centralizer': '24.i1.a1', 'counter': 29, 'group_counter': 155799, 'group_order': 1152, 'label': '6F', 'order': 6, 'powers': [12, 3], 'representative': 33, 'size': 24}
  • id: 108500344
    {'aut_label': '6F', 'centralizer': '24.i1.a1', 'counter': 30, 'group_counter': 155799, 'group_order': 1152, 'label': '6G', 'order': 6, 'powers': [12, 4], 'representative': 17, 'size': 24}
  • id: 108500345
    {'aut_label': '6H', 'centralizer': '48.o1.a1', 'counter': 31, 'group_counter': 155799, 'group_order': 1152, 'label': '6H', 'order': 6, 'powers': [11, 9], 'representative': 786, 'size': 48}
  • id: 108500346
    {'aut_label': '8A1', 'centralizer': '2.c1.a1', 'counter': 32, 'group_counter': 155799, 'group_order': 1152, 'label': '8A1', 'order': 8, 'powers': [14, 32], 'representative': 12, 'size': 2}
  • id: 108500347
    {'aut_label': '8A1', 'centralizer': '2.c1.a1', 'counter': 33, 'group_counter': 155799, 'group_order': 1152, 'label': '8A-1', 'order': 8, 'powers': [14, 33], 'representative': 84, 'size': 2}
  • id: 108500348
    {'aut_label': '8B1', 'centralizer': '6.a1.a1', 'counter': 34, 'group_counter': 155799, 'group_order': 1152, 'label': '8B1', 'order': 8, 'powers': [14, 34], 'representative': 588, 'size': 6}
  • id: 108500349
    {'aut_label': '8B1', 'centralizer': '6.a1.a1', 'counter': 35, 'group_counter': 155799, 'group_order': 1152, 'label': '8B-1', 'order': 8, 'powers': [14, 35], 'representative': 660, 'size': 6}
  • id: 108500350
    {'aut_label': '8C1', 'centralizer': '6.e1.a1', 'counter': 36, 'group_counter': 155799, 'group_order': 1152, 'label': '8C1', 'order': 8, 'powers': [14, 36], 'representative': 13, 'size': 6}
  • id: 108500351
    {'aut_label': '8C1', 'centralizer': '6.e1.a1', 'counter': 37, 'group_counter': 155799, 'group_order': 1152, 'label': '8C-1', 'order': 8, 'powers': [14, 37], 'representative': 85, 'size': 6}
  • id: 108500352
    {'aut_label': '8D1', 'centralizer': '18.g1.a1', 'counter': 38, 'group_counter': 155799, 'group_order': 1152, 'label': '8D1', 'order': 8, 'powers': [14, 38], 'representative': 229, 'size': 18}
  • id: 108500353
    {'aut_label': '8D1', 'centralizer': '18.g1.a1', 'counter': 39, 'group_counter': 155799, 'group_order': 1152, 'label': '8D-1', 'order': 8, 'powers': [14, 39], 'representative': 277, 'size': 18}
  • id: 108500355
    {'aut_label': '12A', 'centralizer': '4.f1.a1', 'counter': 40, 'group_counter': 155799, 'group_order': 1152, 'label': '12A', 'order': 12, 'powers': [24, 14], 'representative': 840, 'size': 4}
  • id: 108500356
    {'aut_label': '12B1', 'centralizer': '8.f1.a1', 'counter': 41, 'group_counter': 155799, 'group_order': 1152, 'label': '12B1', 'order': 12, 'powers': [27, 14], 'representative': 8, 'size': 8}
  • id: 108500357
    {'aut_label': '12B1', 'centralizer': '8.f1.a1', 'counter': 42, 'group_counter': 155799, 'group_order': 1152, 'label': '12B5', 'order': 12, 'powers': [27, 14], 'representative': 40, 'size': 8}
  • id: 108500358
    {'aut_label': '12C', 'centralizer': '12.c1.a1', 'counter': 43, 'group_counter': 155799, 'group_order': 1152, 'label': '12C', 'order': 12, 'powers': [24, 15], 'representative': 216, 'size': 12}
  • id: 108500359
    {'aut_label': '12D1', 'centralizer': '16.k1.a1', 'counter': 44, 'group_counter': 155799, 'group_order': 1152, 'label': '12D1', 'order': 12, 'powers': [28, 14], 'representative': 776, 'size': 16}
  • id: 108500360
    {'aut_label': '12D1', 'centralizer': '16.k1.a1', 'counter': 45, 'group_counter': 155799, 'group_order': 1152, 'label': '12D5', 'order': 12, 'powers': [28, 14], 'representative': 424, 'size': 16}
  • id: 108500361
    {'aut_label': '12E1', 'centralizer': '24.i1.a1', 'counter': 46, 'group_counter': 155799, 'group_order': 1152, 'label': '12E1', 'order': 12, 'powers': [27, 16], 'representative': 9, 'size': 24}
  • id: 108500362
    {'aut_label': '12E1', 'centralizer': '24.i1.a1', 'counter': 47, 'group_counter': 155799, 'group_order': 1152, 'label': '12E5', 'order': 12, 'powers': [27, 16], 'representative': 41, 'size': 24}
  • id: 108500363
    {'aut_label': '12F', 'centralizer': '48.u1.a1', 'counter': 48, 'group_counter': 155799, 'group_order': 1152, 'label': '12F', 'order': 12, 'powers': [25, 18], 'representative': 514, 'size': 48}
  • id: 108500364
    {'aut_label': '12G', 'centralizer': '48.v1.a1', 'counter': 49, 'group_counter': 155799, 'group_order': 1152, 'label': '12G', 'order': 12, 'powers': [24, 19], 'representative': 814, 'size': 48}
  • id: 108500366
    {'aut_label': '12H', 'centralizer': '48.w1.a1', 'counter': 50, 'group_counter': 155799, 'group_order': 1152, 'label': '12H', 'order': 12, 'powers': [26, 20], 'representative': 878, 'size': 48}
  • id: 108500367
    {'aut_label': '24A1', 'centralizer': '4.f1.a1', 'counter': 51, 'group_counter': 155799, 'group_order': 1152, 'label': '24A1', 'order': 24, 'powers': [40, 32], 'representative': 420, 'size': 4}
  • id: 108500368
    {'aut_label': '24A1', 'centralizer': '4.f1.a1', 'counter': 52, 'group_counter': 155799, 'group_order': 1152, 'label': '24A-1', 'order': 24, 'powers': [40, 33], 'representative': 468, 'size': 4}
  • id: 108500369
    {'aut_label': '24B1', 'centralizer': '8.f1.a1', 'counter': 53, 'group_counter': 155799, 'group_order': 1152, 'label': '24B1', 'order': 24, 'powers': [41, 32], 'representative': 4, 'size': 8}
  • id: 108500370
    {'aut_label': '24B1', 'centralizer': '8.f1.a1', 'counter': 54, 'group_counter': 155799, 'group_order': 1152, 'label': '24B-1', 'order': 24, 'powers': [41, 33], 'representative': 52, 'size': 8}
  • id: 108500371
    {'aut_label': '24B1', 'centralizer': '8.f1.a1', 'counter': 55, 'group_counter': 155799, 'group_order': 1152, 'label': '24B5', 'order': 24, 'powers': [42, 33], 'representative': 20, 'size': 8}
  • id: 108500372
    {'aut_label': '24B1', 'centralizer': '8.f1.a1', 'counter': 56, 'group_counter': 155799, 'group_order': 1152, 'label': '24B-5', 'order': 24, 'powers': [42, 32], 'representative': 68, 'size': 8}
  • id: 108500373
    {'aut_label': '24C1', 'centralizer': '12.c1.a1', 'counter': 57, 'group_counter': 155799, 'group_order': 1152, 'label': '24C1', 'order': 24, 'powers': [40, 34], 'representative': 228, 'size': 12}
  • id: 108500374
    {'aut_label': '24C1', 'centralizer': '12.c1.a1', 'counter': 58, 'group_counter': 155799, 'group_order': 1152, 'label': '24C-1', 'order': 24, 'powers': [40, 35], 'representative': 276, 'size': 12}
  • id: 108500375
    {'aut_label': '24D1', 'centralizer': '16.k1.a1', 'counter': 59, 'group_counter': 155799, 'group_order': 1152, 'label': '24D1', 'order': 24, 'powers': [44, 32], 'representative': 388, 'size': 16}
  • id: 108500377
    {'aut_label': '24D1', 'centralizer': '16.k1.a1', 'counter': 60, 'group_counter': 155799, 'group_order': 1152, 'label': '24D-1', 'order': 24, 'powers': [44, 33], 'representative': 436, 'size': 16}
  • id: 108500378
    {'aut_label': '24D1', 'centralizer': '16.k1.a1', 'counter': 61, 'group_counter': 155799, 'group_order': 1152, 'label': '24D5', 'order': 24, 'powers': [45, 33], 'representative': 404, 'size': 16}
  • id: 108500379
    {'aut_label': '24D1', 'centralizer': '16.k1.a1', 'counter': 62, 'group_counter': 155799, 'group_order': 1152, 'label': '24D-5', 'order': 24, 'powers': [45, 32], 'representative': 452, 'size': 16}
  • id: 108500380
    {'aut_label': '24E1', 'centralizer': '24.i1.a1', 'counter': 63, 'group_counter': 155799, 'group_order': 1152, 'label': '24E1', 'order': 24, 'powers': [41, 36], 'representative': 5, 'size': 24}
  • id: 108500381
    {'aut_label': '24E1', 'centralizer': '24.i1.a1', 'counter': 64, 'group_counter': 155799, 'group_order': 1152, 'label': '24E-1', 'order': 24, 'powers': [41, 37], 'representative': 53, 'size': 24}
  • id: 108500382
    {'aut_label': '24E1', 'centralizer': '24.i1.a1', 'counter': 65, 'group_counter': 155799, 'group_order': 1152, 'label': '24E5', 'order': 24, 'powers': [42, 37], 'representative': 21, 'size': 24}
  • id: 108500383
    {'aut_label': '24E1', 'centralizer': '24.i1.a1', 'counter': 66, 'group_counter': 155799, 'group_order': 1152, 'label': '24E-5', 'order': 24, 'powers': [42, 36], 'representative': 69, 'size': 24}
• 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: 3897063
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.1a', '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], 'schur_index': 1}
  • id: 3897074
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.1b', '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], 'schur_index': 1}
  • id: 3897085
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 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: 3897096
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 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: 3897106
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 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: 3897107
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 3897108
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 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: 3897109
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 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: 3897110
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 0, 0, 2, 0, -1, 2, -1, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, -1, -1, -1, 2, -1, 0, 0, -1, 2, 2, 2, 2, 0, 0, 0, 0, -1, 2, 2, -1, -1, -1, 0, 0, -1, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897064
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, -1, -1, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, -1, -1, -1, -1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, 0, 0, 0, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3897065
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 2, 2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -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], 'schur_index': 1}
  • id: 3897066
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -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], 'schur_index': 1}
  • id: 3897067
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 2, -1, -1, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 2, -1, -1, 1, 1, 0, -2, -2, -2, -2, 2, 2, 2, 2, 2, -1, -1, 2, -1, -1, 1, 1, 0, 0, 0, -2, -2, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3897068
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 2, -1, -1, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 2, -1, -1, 1, 1, 0, 2, 2, 2, 2, -2, -2, -2, -2, 2, -1, -1, 2, -1, -1, 1, 1, 0, 0, 0, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3897069
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 0, 0, -2, 0, -1, 2, -1, 2, 2, 0, 0, -2, -2, -2, 0, 0, 0, -1, -1, -1, 2, -1, 0, 0, 1, 2, 2, 2, 2, 0, 0, 0, 0, -1, 2, 2, -1, -1, -1, 0, 0, 1, 1, 1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897070
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 0, 0, -2, 0, -1, 2, -1, 2, 2, 0, 0, 2, 2, -2, 0, 0, 0, -1, -1, -1, 2, -1, 0, 0, 1, -2, -2, -2, -2, 0, 0, 0, 0, -1, 2, 2, -1, -1, -1, 0, 0, -1, -1, 1, 1, 1, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897071
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.2i', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 0, 0, 2, 0, -1, 2, -1, 2, 2, 0, 0, -2, -2, 2, 0, 0, 0, -1, -1, -1, 2, -1, 0, 0, -1, -2, -2, -2, -2, 0, 0, 0, 0, -1, 2, 2, -1, -1, -1, 0, 0, 1, 1, -1, 1, 1, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897072
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.2j', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, -1, -1, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, -1, -1, -1, -1, 0, -2, -2, -2, -2, -2, -2, -2, -2, 2, -1, -1, 2, -1, -1, -1, -1, 0, 0, 0, -2, -2, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3897080
    {'cdim': 3, 'counter': 25, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 3, 3, -1, -1, 1, 1, 3, 0, 0, 3, -1, 3, -1, 1, -1, -1, -1, -1, 1, 3, -1, -1, 0, 0, 0, 0, 1, 3, 3, -1, -1, 3, 3, -1, -1, 3, 0, 0, -1, 0, 0, 0, 0, 1, -1, -1, 3, 3, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897081
    {'cdim': 3, 'counter': 26, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.3b', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 3, 3, -1, -1, -1, -1, 3, 0, 0, 3, -1, 3, -1, -1, 1, 1, 1, 1, -1, 3, -1, -1, 0, 0, 0, 0, -1, 3, 3, -1, -1, 3, 3, -1, -1, 3, 0, 0, -1, 0, 0, 0, 0, -1, 1, 1, 3, 3, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897082
    {'cdim': 3, 'counter': 27, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.3c', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, -1, -3, -3, 1, 1, -1, 1, 3, 0, 0, 3, -1, -3, 1, -1, 1, 1, -1, -1, 1, 3, -1, -1, 0, 0, 0, 0, -1, 3, 3, -1, -1, -3, -3, 1, 1, 3, 0, 0, -1, 0, 0, 0, 0, -1, 1, 1, 3, 3, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897083
    {'cdim': 3, 'counter': 28, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.3d', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, -1, -3, -3, 1, 1, -1, 1, 3, 0, 0, 3, -1, -3, 1, 1, -1, 1, 1, -1, -1, 3, -1, -1, 0, 0, 0, 0, -1, -3, -3, 1, 1, 3, 3, -1, -1, 3, 0, 0, -1, 0, 0, 0, 0, 1, -1, 1, -3, -3, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897084
    {'cdim': 3, 'counter': 29, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.3e', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, -1, -3, -3, 1, 1, 1, -1, 3, 0, 0, 3, -1, -3, 1, -1, 1, -1, -1, 1, 1, 3, -1, -1, 0, 0, 0, 0, 1, -3, -3, 1, 1, 3, 3, -1, -1, 3, 0, 0, -1, 0, 0, 0, 0, -1, 1, -1, -3, -3, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897086
    {'cdim': 3, 'counter': 30, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.3f', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, -1, -3, -3, 1, 1, 1, -1, 3, 0, 0, 3, -1, -3, 1, 1, -1, -1, 1, 1, -1, 3, -1, -1, 0, 0, 0, 0, 1, 3, 3, -1, -1, -3, -3, 1, 1, 3, 0, 0, -1, 0, 0, 0, 0, 1, -1, -1, 3, 3, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897087
    {'cdim': 3, 'counter': 31, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.3g', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 3, 3, -1, -1, -1, -1, 3, 0, 0, 3, -1, 3, -1, 1, -1, 1, -1, 1, 1, 3, -1, -1, 0, 0, 0, 0, -1, -3, -3, 1, 1, -3, -3, 1, 1, 3, 0, 0, -1, 0, 0, 0, 0, 1, -1, 1, -3, -3, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897088
    {'cdim': 3, 'counter': 32, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.3h', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 3, 3, -1, -1, 1, 1, 3, 0, 0, 3, -1, 3, -1, -1, 1, -1, 1, -1, -1, 3, -1, -1, 0, 0, 0, 0, 1, -3, -3, 1, 1, -3, -3, 1, 1, 3, 0, 0, -1, 0, 0, 0, 0, -1, 1, -1, -3, -3, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897073
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.2k', 'multiplicity': 2, 'nt': [8, 8], 'qdim': 4, 'qvalues': [4, -4, -4, 4, -4, 4, 4, -4, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, -4, -4, 4, -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], 'schur_index': 1}
  • id: 3897075
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.2l', 'multiplicity': 2, 'nt': [8, 8], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 4, -4, -4, 4, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, -4, -4, -4, 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], 'schur_index': 1}
  • id: 3897076
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.2m', 'multiplicity': 2, 'nt': [12, 12], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, -4, -4, 0, 0, 4, -2, -2, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 4, 4, 4, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 2, -4, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897077
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.2n', 'multiplicity': 2, 'nt': [12, 12], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 4, -2, -2, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 4, 4, 4, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 2, -4, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897089
    {'cdim': 4, 'counter': 33, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.4a', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, 0, 0, -2, -2, 1, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 1, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, -2, -2, -2, -2, 1, 1, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897090
    {'cdim': 4, 'counter': 34, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.4b', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, 0, 0, -2, 4, -2, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, -4, 2, 2, 2, 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: 3897091
    {'cdim': 4, 'counter': 35, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.4c', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, 0, 0, -2, -2, 1, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 1, 0, 0, 0, -4, -4, -4, -4, 0, 0, 0, 0, -2, -2, -2, -2, 1, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897095
    {'cdim': 6, 'counter': 39, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.6a', 'multiplicity': 1, 'nt': [12, 54], 'qdim': 6, 'qvalues': [6, 6, -2, -2, -6, -6, 2, 2, 0, 0, 6, 0, 0, -6, 2, 6, -2, 0, 0, 0, 0, 0, 0, 6, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 2, 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: 3897097
    {'cdim': 6, 'counter': 40, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.6b', 'multiplicity': 1, 'nt': [12, 54], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 6, 6, -2, -2, 0, 0, 6, 0, 0, -6, 2, -6, 2, 0, 0, 0, 0, 0, 0, 6, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 2, 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: 3897098
    {'cdim': 6, 'counter': 41, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.6c', 'multiplicity': 1, 'nt': [12, 83], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 0, 0, 0, 0, 2, 0, -3, 0, 0, 6, -2, 0, 0, 2, -2, -2, 0, 0, 0, -3, 1, 1, 0, 0, 0, 0, -1, 6, 6, -2, -2, 0, 0, 0, 0, -3, 0, 0, 1, 0, 0, 0, 0, -1, 1, 1, -3, -3, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897099
    {'cdim': 6, 'counter': 42, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.6d', 'multiplicity': 1, 'nt': [18, 69], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 0, 0, 0, 0, -2, 0, -3, 0, 0, 6, -2, 0, 0, -2, 2, 2, 0, 0, 0, -3, 1, 1, 0, 0, 0, 0, 1, 6, 6, -2, -2, 0, 0, 0, 0, -3, 0, 0, 1, 0, 0, 0, 0, 1, -1, -1, -3, -3, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897100
    {'cdim': 6, 'counter': 43, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.6e', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 0, 0, 0, 0, -2, 0, -3, 0, 0, 6, -2, 0, 0, 2, -2, 2, 0, 0, 0, -3, 1, 1, 0, 0, 0, 0, 1, -6, -6, 2, 2, 0, 0, 0, 0, -3, 0, 0, 1, 0, 0, 0, 0, -1, 1, -1, 3, 3, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897101
    {'cdim': 6, 'counter': 44, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.6f', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 0, 0, 0, 0, 2, 0, -3, 0, 0, 6, -2, 0, 0, -2, 2, -2, 0, 0, 0, -3, 1, 1, 0, 0, 0, 0, -1, -6, -6, 2, 2, 0, 0, 0, 0, -3, 0, 0, 1, 0, 0, 0, 0, 1, -1, 1, 3, 3, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3897078
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.2o', 'multiplicity': 4, 'nt': [24, 35], 'qdim': 8, 'qvalues': [8, -8, -8, 8, -8, 8, 8, -8, 0, 0, 8, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, -8, 4, 4, -4, 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], 'schur_index': 1}
  • id: 3897079
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.2p', 'multiplicity': 4, 'nt': [24, 35], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 8, -8, -8, 8, 0, 0, 8, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, -8, 4, 4, 4, -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], 'schur_index': 1}
  • id: 3897092
    {'cdim': 4, 'counter': 36, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.4d', 'multiplicity': 2, 'nt': [24, 142], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, 0, 0, -4, 8, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, -8, 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], 'schur_index': 1}
  • id: 3897093
    {'cdim': 4, 'counter': 37, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.4e', 'multiplicity': 2, 'nt': [24, 229], 'qdim': 8, 'qvalues': [8, 8, 8, 8, 0, 0, 0, 0, 0, 0, -4, -4, 2, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, -2, -2, 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: 3897102
    {'cdim': 6, 'counter': 45, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.6g', 'multiplicity': 2, 'nt': [24, 325], 'qdim': 12, 'qvalues': [12, -12, 4, -4, -12, 12, -4, 4, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -4, 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], 'schur_index': 1}
  • id: 3897103
    {'cdim': 6, 'counter': 46, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.6h', 'multiplicity': 2, 'nt': [24, 325], 'qdim': 12, 'qvalues': [12, -12, 4, -4, 12, -12, 4, -4, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -4, 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], 'schur_index': 1}
  • id: 3897104
    {'cdim': 12, 'counter': 47, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.12a', 'multiplicity': 1, 'nt': [36, 805], 'qdim': 12, 'qvalues': [12, 12, -4, -4, 0, 0, 0, 0, 0, 0, -6, 0, 0, -12, 4, 0, 0, 0, 0, 0, 0, 0, 0, -6, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, -2, 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: 3897094
    {'cdim': 4, 'counter': 38, 'faithful': False, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.4f', 'multiplicity': 4, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, -16, -16, 16, 0, 0, 0, 0, 0, 0, -8, -8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, 8, 8, -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], 'schur_index': 1}
  • id: 3897105
    {'cdim': 12, 'counter': 48, 'faithful': True, 'group': '1152.155799', 'group_order': 1152, 'image': None, 'label': '1152.155799.12b', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -24, 8, -8, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 4, -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], '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: 5408018
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1152, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 1152, 'label': '1152.155799.1a', '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]]]}
  • id: 5408029
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1152, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.a1', 'kernel_order': 576, 'label': '1152.155799.1b', '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]]]}
  • id: 5408040
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1152, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.a1', 'kernel_order': 576, 'label': '1152.155799.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 5408051
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1152, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 576, 'label': '1152.155799.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 5408062
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1152, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 576, 'label': '1152.155799.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 5408073
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1152, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 576, 'label': '1152.155799.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 5408081
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1152, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 576, 'label': '1152.155799.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 5408082
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1152, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 576, 'label': '1152.155799.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 5408083
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 192, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.b1.a1', 'kernel_order': 192, 'label': '1152.155799.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408019
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 192, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 192, 'label': '1152.155799.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5408020
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 288, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1.a1', 'kernel_order': 144, 'label': '1152.155799.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 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]], [[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]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408021
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 288, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1.a1', 'kernel_order': 144, 'label': '1152.155799.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 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]], [[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]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408022
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 192, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.d1.a1', 'kernel_order': 96, 'label': '1152.155799.2e', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5408023
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 192, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1.a1', 'kernel_order': 96, 'label': '1152.155799.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5408024
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 192, 'counter': 15, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.f1.a1', 'kernel_order': 96, 'label': '1152.155799.2g', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408025
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 192, 'counter': 16, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.e1.a1', 'kernel_order': 96, 'label': '1152.155799.2h', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408026
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 192, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.a1', 'kernel_order': 96, 'label': '1152.155799.2i', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408027
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 192, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 96, 'label': '1152.155799.2j', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5408028
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 144, 'counter': 19, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1.a1', 'kernel_order': 72, 'label': '1152.155799.2k1', 'nt': [8, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[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, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]]]}
  • id: 5408030
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 144, 'counter': 20, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1.a1', 'kernel_order': 72, 'label': '1152.155799.2k2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[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, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]]]}
  • id: 5408031
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 144, 'counter': 21, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1.b1', 'kernel_order': 72, 'label': '1152.155799.2l1', 'nt': [8, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[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, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]]]}
  • id: 5408032
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 144, 'counter': 22, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1.b1', 'kernel_order': 72, 'label': '1152.155799.2l2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[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, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]]]}
  • id: 5408033
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 96, 'counter': 23, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.d1.a1', 'kernel_order': 48, 'label': '1152.155799.2m1', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 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]], [[0, 0]], [[0, 0]], [[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]]]}
  • id: 5408034
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 96, 'counter': 24, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.d1.a1', 'kernel_order': 48, 'label': '1152.155799.2m2', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 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]], [[0, 0]], [[0, 0]], [[-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]]]}
  • id: 5408035
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 96, 'counter': 25, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 48, 'label': '1152.155799.2n1', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 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]], [[0, 0]], [[0, 0]], [[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]]]}
  • id: 5408036
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 96, 'counter': 26, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 48, 'label': '1152.155799.2n2', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 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]], [[0, 0]], [[0, 0]], [[-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]]]}
  • id: 5408037
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 48, 'counter': 27, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [1, 0, 4, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '48.6', 'image_order': 48, 'indicator': 0, 'kernel': '48.f1.a1', 'kernel_order': 24, 'label': '1152.155799.2o1', 'nt': [24, 35], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]]]}
  • id: 5408038
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 48, 'counter': 28, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [1, 0, 4, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '48.6', 'image_order': 48, 'indicator': 0, 'kernel': '48.f1.a1', 'kernel_order': 24, 'label': '1152.155799.2o2', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]]]}
  • id: 5408039
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 48, 'counter': 29, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [1, 0, 4, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '48.6', 'image_order': 48, 'indicator': 0, 'kernel': '48.f1.a1', 'kernel_order': 24, 'label': '1152.155799.2o3', 'nt': [24, 35], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]]]}
  • id: 5408041
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 48, 'counter': 30, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [1, 0, 4, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '48.6', 'image_order': 48, 'indicator': 0, 'kernel': '48.f1.a1', 'kernel_order': 24, 'label': '1152.155799.2o4', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]]]}
  • id: 5408042
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 48, 'counter': 31, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [1, 0, 4, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '48.6', 'image_order': 48, 'indicator': 0, 'kernel': '48.f1.b1', 'kernel_order': 24, 'label': '1152.155799.2p1', 'nt': [24, 35], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]]]}
  • id: 5408043
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 48, 'counter': 32, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [1, 0, 4, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '48.6', 'image_order': 48, 'indicator': 0, 'kernel': '48.f1.b1', 'kernel_order': 24, 'label': '1152.155799.2p2', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]]]}
  • id: 5408044
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 48, 'counter': 33, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [1, 0, 4, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '48.6', 'image_order': 48, 'indicator': 0, 'kernel': '48.f1.b1', 'kernel_order': 24, 'label': '1152.155799.2p3', 'nt': [24, 35], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]]]}
  • id: 5408045
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 48, 'counter': 34, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [1, 0, 4, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '48.6', 'image_order': 48, 'indicator': 0, 'kernel': '48.f1.b1', 'kernel_order': 24, 'label': '1152.155799.2p4', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]]]}
  • id: 5408046
    {'center': '24.b1.a1', 'center_index': 24, 'center_order': 48, 'counter': 35, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.b1.a1', 'kernel_order': 48, 'label': '1152.155799.3a', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408047
    {'center': '24.b1.a1', 'center_index': 24, 'center_order': 48, 'counter': 36, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.b1.a1', 'kernel_order': 48, 'label': '1152.155799.3b', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408048
    {'center': '24.b1.a1', 'center_index': 24, 'center_order': 48, 'counter': 37, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.d1.a1', 'kernel_order': 24, 'label': '1152.155799.3c', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408049
    {'center': '24.b1.a1', 'center_index': 24, 'center_order': 48, 'counter': 38, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.e1.a1', 'kernel_order': 24, 'label': '1152.155799.3d', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408050
    {'center': '24.b1.a1', 'center_index': 24, 'center_order': 48, 'counter': 39, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.e1.a1', 'kernel_order': 24, 'label': '1152.155799.3e', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408052
    {'center': '24.b1.a1', 'center_index': 24, 'center_order': 48, 'counter': 40, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.d1.a1', 'kernel_order': 24, 'label': '1152.155799.3f', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408053
    {'center': '24.b1.a1', 'center_index': 24, 'center_order': 48, 'counter': 41, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1.a1', 'kernel_order': 24, 'label': '1152.155799.3g', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408054
    {'center': '24.b1.a1', 'center_index': 24, 'center_order': 48, 'counter': 42, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1.a1', 'kernel_order': 24, 'label': '1152.155799.3h', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408055
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 32, 'counter': 43, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1.a1', 'kernel_order': 32, 'label': '1152.155799.4a', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[4, 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]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408056
    {'center': '24.e1.a1', 'center_index': 24, 'center_order': 48, 'counter': 44, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '48.38', 'image_order': 48, 'indicator': 1, 'kernel': '48.c1.a1', 'kernel_order': 24, 'label': '1152.155799.4b', 'nt': [12, 28], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 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]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408057
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 32, 'counter': 45, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '72.46', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1.a1', 'kernel_order': 16, 'label': '1152.155799.4c', 'nt': [12, 37], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[4, 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]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408058
    {'center': '48.c1.a1', 'center_index': 48, 'center_order': 24, 'counter': 46, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '96.120', 'image_order': 96, 'indicator': 0, 'kernel': '96.e1.a1', 'kernel_order': 12, 'label': '1152.155799.4d1', 'nt': [24, 142], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 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]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408059
    {'center': '48.c1.a1', 'center_index': 48, 'center_order': 24, 'counter': 47, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '96.120', 'image_order': 96, 'indicator': 0, 'kernel': '96.e1.a1', 'kernel_order': 12, 'label': '1152.155799.4d2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 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]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408060
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 16, 'counter': 48, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [-3, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '144.144', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1.a1', 'kernel_order': 8, 'label': '1152.155799.4e1', 'nt': [24, 229], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-4, 0]], [[-4, 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]], [[1, 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, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408061
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 16, 'counter': 49, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [-3, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '144.144', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1.a1', 'kernel_order': 8, 'label': '1152.155799.4e2', 'nt': [24, 229], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-4, 0]], [[-4, 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]], [[1, 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, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408063
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 8, 'counter': 50, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [1, 0, 4, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '288.440', 'image_order': 288, 'indicator': 0, 'kernel': '288.b1.a1', 'kernel_order': 4, 'label': '1152.155799.4f1', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 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]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [-2, 3], [-2, 5]], [[-2, 1], [2, 3], [2, 5]], [[2, 1], [-2, 3], [-2, 5]], [[-2, 1], [2, 3], [2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-2, 1], [2, 3], [-2, 7]], [[-2, 5], [-2, 7]], [[2, 5], [2, 7]], [[2, 1], [-2, 3], [2, 7]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408064
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 8, 'counter': 51, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [1, 0, 4, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '288.440', 'image_order': 288, 'indicator': 0, 'kernel': '288.b1.a1', 'kernel_order': 4, 'label': '1152.155799.4f2', 'nt': [48, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 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]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [2, 3], [2, 5]], [[2, 1], [-2, 3], [-2, 5]], [[-2, 1], [2, 3], [2, 5]], [[2, 1], [-2, 3], [-2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[2, 1], [-2, 3], [2, 7]], [[2, 5], [2, 7]], [[-2, 5], [-2, 7]], [[-2, 1], [2, 3], [-2, 7]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408065
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 8, 'counter': 52, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [1, 0, 4, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '288.440', 'image_order': 288, 'indicator': 0, 'kernel': '288.b1.a1', 'kernel_order': 4, 'label': '1152.155799.4f3', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 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]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [-2, 3], [-2, 5]], [[-2, 1], [2, 3], [2, 5]], [[2, 1], [-2, 3], [-2, 5]], [[-2, 1], [2, 3], [2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[2, 5], [2, 7]], [[2, 1], [-2, 3], [2, 7]], [[-2, 1], [2, 3], [-2, 7]], [[-2, 5], [-2, 7]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[1, 1], [-1, 3], [1, 7]], [[1, 5], [1, 7]], [[-1, 5], [-1, 7]], [[-1, 1], [1, 3], [-1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408066
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 8, 'counter': 53, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [1, 0, 4, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '288.440', 'image_order': 288, 'indicator': 0, 'kernel': '288.b1.a1', 'kernel_order': 4, 'label': '1152.155799.4f4', 'nt': [48, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 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]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [2, 3], [2, 5]], [[2, 1], [-2, 3], [-2, 5]], [[-2, 1], [2, 3], [2, 5]], [[2, 1], [-2, 3], [-2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-2, 5], [-2, 7]], [[-2, 1], [2, 3], [-2, 7]], [[2, 1], [-2, 3], [2, 7]], [[2, 5], [2, 7]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[-1, 1], [1, 3], [-1, 7]], [[-1, 5], [-1, 7]], [[1, 5], [1, 7]], [[1, 1], [-1, 3], [1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408067
    {'center': '48.a1.a1', 'center_index': 48, 'center_order': 24, 'counter': 54, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '96.187', 'image_order': 96, 'indicator': 1, 'kernel': '96.c1.a1', 'kernel_order': 12, 'label': '1152.155799.6a', 'nt': [12, 54], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-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]], [[-6, 0]], [[0, 0]], [[0, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408068
    {'center': '48.a1.a1', 'center_index': 48, 'center_order': 24, 'counter': 55, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '96.187', 'image_order': 96, 'indicator': 1, 'kernel': '96.a1.a1', 'kernel_order': 12, 'label': '1152.155799.6b', 'nt': [12, 54], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-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]], [[-6, 0]], [[0, 0]], [[0, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408069
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 8, 'counter': 56, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': '144.b1.a1', 'kernel_order': 8, 'label': '1152.155799.6c', 'nt': [12, 83], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408070
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 8, 'counter': 57, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': '144.b1.a1', 'kernel_order': 8, 'label': '1152.155799.6d', 'nt': [18, 69], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408071
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 8, 'counter': 58, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '288.1028', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1.a1', 'kernel_order': 4, 'label': '1152.155799.6e', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408072
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 8, 'counter': 59, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '288.1028', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1.a1', 'kernel_order': 4, 'label': '1152.155799.6f', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408074
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 12, 'counter': 60, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [2, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '192.960', 'image_order': 192, 'indicator': 0, 'kernel': '192.b1.a1', 'kernel_order': 6, 'label': '1152.155799.6g1', 'nt': [24, 325], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[-6, 0]], [[6, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[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]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, 3]], [[3, 1], [3, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-3, 1], [-3, 3]], [[3, 1], [3, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, 3]], [[3, 1], [3, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408075
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 12, 'counter': 61, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [2, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '192.960', 'image_order': 192, 'indicator': 0, 'kernel': '192.b1.a1', 'kernel_order': 6, 'label': '1152.155799.6g2', 'nt': [24, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[-6, 0]], [[6, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[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]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, 3]], [[-3, 1], [-3, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[3, 1], [3, 3]], [[-3, 1], [-3, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, 3]], [[-3, 1], [-3, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408076
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 12, 'counter': 62, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [2, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '192.960', 'image_order': 192, 'indicator': 0, 'kernel': '192.b1.b1', 'kernel_order': 6, 'label': '1152.155799.6h1', 'nt': [24, 325], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[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]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, 3]], [[3, 1], [3, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[3, 1], [3, 3]], [[-3, 1], [-3, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, 3]], [[3, 1], [3, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408077
    {'center': '96.a1.a1', 'center_index': 96, 'center_order': 12, 'counter': 63, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [2, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '192.960', 'image_order': 192, 'indicator': 0, 'kernel': '192.b1.b1', 'kernel_order': 6, 'label': '1152.155799.6h2', 'nt': [24, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[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]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, 3]], [[-3, 1], [-3, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-3, 1], [-3, 3]], [[3, 1], [3, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, 3]], [[-3, 1], [-3, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408078
    {'center': '288.a1.a1', 'center_index': 288, 'center_order': 4, 'counter': 64, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '576.8312', 'image_order': 576, 'indicator': 1, 'kernel': '576.a1.a1', 'kernel_order': 2, 'label': '1152.155799.12a', 'nt': [36, 805], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[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]], [[6, 0]], [[0, 0]], [[0, 0]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408079
    {'center': '576.a1.a1', 'center_index': 576, 'center_order': 2, 'counter': 65, 'cyclotomic_n': 8, 'dim': 12, 'faithful': True, 'field': [2, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '1152.155799', 'image_order': 1152, 'indicator': 0, 'kernel': '1152.a1.a1', 'kernel_order': 1, 'label': '1152.155799.12b1', 'nt': [72, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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]], [[6, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 1], [-6, 3]], [[6, 1], [6, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 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]], [[3, 1], [3, 3]], [[-3, 1], [-3, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5408080
    {'center': '576.a1.a1', 'center_index': 576, 'center_order': 2, 'counter': 66, 'cyclotomic_n': 8, 'dim': 12, 'faithful': True, 'field': [2, 0, 1], 'group': '1152.155799', 'group_counter': 155799, 'group_order': 1152, 'image': None, 'image_isoclass': '1152.155799', 'image_order': 1152, 'indicator': 0, 'kernel': '1152.a1.a1', 'kernel_order': 1, 'label': '1152.155799.12b2', 'nt': [72, 2], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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]], [[6, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 1], [6, 3]], [[-6, 1], [-6, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 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]], [[-3, 1], [-3, 3]], [[3, 1], [3, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[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: 60968036
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1152, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '1152.155799.1.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': '1152.155799', 'subgroup_hash': 7082498570119804226, 'subgroup_order': 1152, 'subgroup_tex': 'S_3\\times C_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968147
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 576, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '576.8312', 'subgroup_hash': 8312, 'subgroup_order': 576, 'subgroup_tex': 'S_3\\times C_4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968258
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 576, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '576.8305', 'subgroup_hash': 8305, 'subgroup_order': 576, 'subgroup_tex': 'S_3\\times A_4:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 60968369
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 576, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '576.5568', 'subgroup_hash': 5568, 'subgroup_order': 576, 'subgroup_tex': 'S_3\\times C_8\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968480
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 576, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '576.5469', 'subgroup_hash': 5469, 'subgroup_order': 576, 'subgroup_tex': 'C_{24}:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968591
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 576, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '576.5059', 'subgroup_hash': 5059, 'subgroup_order': 576, 'subgroup_tex': 'C_{12}.(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 60968625
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 576, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.2.f1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '576.5060', 'subgroup_hash': 5060, 'subgroup_order': 576, 'subgroup_tex': 'C_{12}.(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 60968636
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 576, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.2.g1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '576.5517', 'subgroup_hash': 5517, 'subgroup_order': 576, 'subgroup_tex': 'C_{24}:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968647
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 192, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18014', 'subgroup_hash': 18014, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4.D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 60968037
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 192, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.3.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.13231', 'subgroup_hash': 13231, 'subgroup_order': 384, 'subgroup_tex': 'S_3\\times C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968048
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 288, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '288.919', 'subgroup_hash': 919, 'subgroup_order': 288, 'subgroup_tex': 'C_4\\times S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968059
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 288, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '288.898', 'subgroup_hash': 898, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968070
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 288, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '288.909', 'subgroup_hash': 909, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968081
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 288, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '288.896', 'subgroup_hash': 896, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968092
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 288, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '288.907', 'subgroup_hash': 907, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968103
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 288, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '288.637', 'subgroup_hash': 637, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\times C_{24}', 'supersolvable': False, 'sylow': 0}
  • id: 60968114
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 288, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '288.408', 'subgroup_hash': 408, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\times C_3:C_8', 'supersolvable': False, 'sylow': 0}
  • id: 60968125
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968136
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '288.856', 'subgroup_hash': 856, 'subgroup_order': 288, 'subgroup_tex': 'D_6.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968148
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 48, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.4.j1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '288.440', 'subgroup_hash': 440, 'subgroup_order': 288, 'subgroup_tex': 'C_{24}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968159
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.4.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '288.855', 'subgroup_hash': 855, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 60968170
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.4.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '288.852', 'subgroup_hash': 852, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 60968181
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 192, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.6.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.1295', 'subgroup_hash': 1295, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60968192
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': True, 'core_order': 192, 'counter': 24, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1152.155799.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.960', 'subgroup_hash': 960, 'subgroup_order': 192, 'subgroup_tex': 'C_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968203
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1470', 'subgroup_hash': 1470, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 60968214
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1468', 'subgroup_hash': 1468, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4.D_6', 'supersolvable': False, 'sylow': 0}
  • id: 60968225
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 96, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1010', 'subgroup_hash': 1010, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:C_{24}', 'supersolvable': False, 'sylow': 0}
  • id: 60968236
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '192.1317', 'subgroup_hash': 1317, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968247
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.328', 'subgroup_hash': 328, 'subgroup_order': 192, 'subgroup_tex': 'D_6.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968259
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.6.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': '192.360', 'subgroup_hash': 360, 'subgroup_order': 192, 'subgroup_tex': 'D_6.Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968270
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.6.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': '192.418', 'subgroup_hash': 418, 'subgroup_order': 192, 'subgroup_tex': 'D_6.\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968281
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.6.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': '192.1163', 'subgroup_hash': 1163, 'subgroup_order': 192, 'subgroup_tex': 'S_3\\times C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968292
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.6.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': '192.1185', 'subgroup_hash': 1185, 'subgroup_order': 192, 'subgroup_tex': 'S_3\\times C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968303
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.6.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '192.730', 'subgroup_hash': 730, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968314
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.6.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '192.337', 'subgroup_hash': 337, 'subgroup_order': 192, 'subgroup_tex': 'D_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968325
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.6.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '192.366', 'subgroup_hash': 366, 'subgroup_order': 192, 'subgroup_tex': 'D_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968336
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.6.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '192.423', 'subgroup_hash': 423, 'subgroup_order': 192, 'subgroup_tex': 'C_8:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968347
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 96, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.6.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.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': 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': '192.898', 'subgroup_hash': 898, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968358
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.6.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '192.600', 'subgroup_hash': 600, 'subgroup_order': 192, 'subgroup_tex': '(C_2\\times C_6):\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968370
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.6.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '192.960', 'subgroup_hash': 960, 'subgroup_order': 192, 'subgroup_tex': 'C_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968381
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.6.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '192.607', 'subgroup_hash': 607, 'subgroup_order': 192, 'subgroup_tex': '(C_2\\times C_6):\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968392
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.6.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '192.673', 'subgroup_hash': 673, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968403
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.6.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '192.960', 'subgroup_hash': 960, 'subgroup_order': 192, 'subgroup_tex': 'C_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968414
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.6.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '192.960', 'subgroup_hash': 960, 'subgroup_order': 192, 'subgroup_tex': 'C_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968425
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.6.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '192.960', 'subgroup_hash': 960, 'subgroup_order': 192, 'subgroup_tex': 'C_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968436
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 144, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 60968447
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 144, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.155', 'subgroup_hash': 155, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968458
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 144, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.129', 'subgroup_hash': 129, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times C_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968469
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968481
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '144.137', 'subgroup_hash': 137, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968492
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 48, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '144.69', 'subgroup_hash': 69, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60968503
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968514
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968525
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '144.123', 'subgroup_hash': 123, 'subgroup_order': 144, 'subgroup_tex': 'A_4:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 60968536
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '144.126', 'subgroup_hash': 126, 'subgroup_order': 144, 'subgroup_tex': 'C_6.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968547
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '144.71', 'subgroup_hash': 71, 'subgroup_order': 144, 'subgroup_tex': 'C_{24}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968558
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '144.59', 'subgroup_hash': 59, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968569
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.8.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '144.60', 'subgroup_hash': 60, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968580
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.8.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '144.87', 'subgroup_hash': 87, 'subgroup_order': 144, 'subgroup_tex': 'C_{24}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60968592
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.8.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968603
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.8.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968614
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1152.155799.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '128.1779', 'subgroup_hash': 1779, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3:\\SD_{16}', 'supersolvable': True, 'sylow': 2}
  • id: 60968618
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 96, 'counter': 63, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.206', 'subgroup_hash': 206, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60968619
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 96, 'counter': 64, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.187', 'subgroup_hash': 187, 'subgroup_order': 96, 'subgroup_tex': 'C_4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968620
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 96, 'counter': 65, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.176', 'subgroup_hash': 176, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60968621
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 96, 'counter': 66, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.127', 'subgroup_hash': 127, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60968622
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 96, 'counter': 67, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.185', 'subgroup_hash': 185, 'subgroup_order': 96, 'subgroup_tex': 'A_4:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 60968623
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 96, 'counter': 68, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.73', 'subgroup_hash': 73, 'subgroup_order': 96, 'subgroup_tex': 'C_8\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968624
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968626
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.196', 'subgroup_hash': 196, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 60968627
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.194', 'subgroup_hash': 194, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968628
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.109', 'subgroup_hash': 109, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968629
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968630
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968631
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '96.98', 'subgroup_hash': 98, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968632
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '96.212', 'subgroup_hash': 212, 'subgroup_order': 96, 'subgroup_tex': 'Q_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968633
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '96.98', 'subgroup_hash': 98, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968634
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 48, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '96.106', 'subgroup_hash': 106, 'subgroup_order': 96, 'subgroup_tex': 'C_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968635
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 24, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '96.106', 'subgroup_hash': 106, 'subgroup_order': 96, 'subgroup_tex': 'C_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968637
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '96.98', 'subgroup_hash': 98, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968638
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968639
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968640
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968641
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968642
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '96.91', 'subgroup_hash': 91, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968643
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '96.145', 'subgroup_hash': 145, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968644
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '96.102', 'subgroup_hash': 102, 'subgroup_order': 96, 'subgroup_tex': 'C_4:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968645
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.z1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.153', 'subgroup_hash': 153, 'subgroup_order': 96, 'subgroup_tex': 'D_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968646
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ba1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.104', 'subgroup_hash': 104, 'subgroup_order': 96, 'subgroup_tex': 'D_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968648
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 24, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bb1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.106', 'subgroup_hash': 106, 'subgroup_order': 96, 'subgroup_tex': 'C_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968649
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 24, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bc1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.106', 'subgroup_hash': 106, 'subgroup_order': 96, 'subgroup_tex': 'C_8\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968650
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bd1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.103', 'subgroup_hash': 103, 'subgroup_order': 96, 'subgroup_tex': 'D_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968651
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.be1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.180', 'subgroup_hash': 180, 'subgroup_order': 96, 'subgroup_tex': 'C_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968652
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bf1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.52', 'subgroup_hash': 52, 'subgroup_order': 96, 'subgroup_tex': 'D_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968653
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bg1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.39', 'subgroup_hash': 39, 'subgroup_order': 96, 'subgroup_tex': 'C_6.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968654
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bh1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.140', 'subgroup_hash': 140, 'subgroup_order': 96, 'subgroup_tex': 'C_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968655
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bi1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.148', 'subgroup_hash': 148, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968656
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bj1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.16', 'subgroup_hash': 16, 'subgroup_order': 96, 'subgroup_tex': 'D_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968657
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bk1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.28', 'subgroup_hash': 28, 'subgroup_order': 96, 'subgroup_tex': 'D_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968038
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bl1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.109', 'subgroup_hash': 109, 'subgroup_order': 96, 'subgroup_tex': 'C_8:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968039
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bm1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.53', 'subgroup_hash': 53, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968040
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bn1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.56', 'subgroup_hash': 56, 'subgroup_order': 96, 'subgroup_tex': 'C_8:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968041
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bo1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.15', 'subgroup_hash': 15, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968042
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bp1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.17', 'subgroup_hash': 17, 'subgroup_order': 96, 'subgroup_tex': 'C_4.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968043
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bq1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.42', 'subgroup_hash': 42, 'subgroup_order': 96, 'subgroup_tex': 'C_6.Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968044
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.br1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.15', 'subgroup_hash': 15, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968045
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bs1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.24', 'subgroup_hash': 24, 'subgroup_order': 96, 'subgroup_tex': 'C_{24}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968046
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bt1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.23', 'subgroup_hash': 23, 'subgroup_order': 96, 'subgroup_tex': 'C_6.Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968047
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bu1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.146', 'subgroup_hash': 146, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968049
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bv1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.168', 'subgroup_hash': 168, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968050
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bw1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.187', 'subgroup_hash': 187, 'subgroup_order': 96, 'subgroup_tex': 'C_4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968051
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bx1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.137', 'subgroup_hash': 137, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968052
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.by1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.187', 'subgroup_hash': 187, 'subgroup_order': 96, 'subgroup_tex': 'C_4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bz1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.187', 'subgroup_hash': 187, 'subgroup_order': 96, 'subgroup_tex': 'C_4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968054
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.ca1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.169', 'subgroup_hash': 169, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968055
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cb1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.131', 'subgroup_hash': 131, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968056
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cc1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.85', 'subgroup_hash': 85, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968057
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cd1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.185', 'subgroup_hash': 185, 'subgroup_order': 96, 'subgroup_tex': 'A_4:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 60968058
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ce1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.73', 'subgroup_hash': 73, 'subgroup_order': 96, 'subgroup_tex': 'C_8\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968060
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cf1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.185', 'subgroup_hash': 185, 'subgroup_order': 96, 'subgroup_tex': 'A_4:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 60968061
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cg1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.185', 'subgroup_hash': 185, 'subgroup_order': 96, 'subgroup_tex': 'A_4:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 60968062
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 32, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ch1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.73', 'subgroup_hash': 73, 'subgroup_order': 96, 'subgroup_tex': 'C_8\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968063
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ci1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968064
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.12.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cj1.a1', 'outer_equivalence': False, 'perfect': False, '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': '96.120', 'subgroup_hash': 120, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968065
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 72, 'counter': 125, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968066
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 126, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968067
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 127, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.16.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968068
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968069
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968071
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968072
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968073
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968074
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.33', 'subgroup_hash': 33, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968075
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.26', 'subgroup_hash': 26, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968076
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.31', 'subgroup_hash': 31, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968077
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 24, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.16.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.14', 'subgroup_hash': 14, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60968078
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.16.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.12', 'subgroup_hash': 12, 'subgroup_order': 72, 'subgroup_tex': 'C_3:C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60968079
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.16.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.24', 'subgroup_hash': 24, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968080
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.16.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': 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: 60968082
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.16.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': 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: 60968083
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 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': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968084
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.95', 'subgroup_hash': 95, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968085
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.96', 'subgroup_hash': 96, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2.Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968086
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.106', 'subgroup_hash': 106, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968087
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.18.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.203', 'subgroup_hash': 203, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968088
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.18.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '64.204', 'subgroup_hash': 204, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968089
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 32, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.18.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '64.246', 'subgroup_hash': 246, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968090
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.18.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '64.146', 'subgroup_hash': 146, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968091
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.18.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '64.146', 'subgroup_hash': 146, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968093
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.18.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '64.146', 'subgroup_hash': 146, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968094
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.18.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '64.146', 'subgroup_hash': 146, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968095
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 32, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.18.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '64.146', 'subgroup_hash': 146, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968096
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.18.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '64.146', 'subgroup_hash': 146, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968097
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.18.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '64.146', 'subgroup_hash': 146, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968098
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.18.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '64.146', 'subgroup_hash': 146, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968099
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 48, 'counter': 156, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968100
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 48, 'counter': 157, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.b1.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': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968101
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 48, 'counter': 158, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968102
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 48, 'counter': 159, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60968104
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 48, 'counter': 160, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968105
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968106
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968107
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968108
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '48.23', 'subgroup_hash': 23, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60968109
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968110
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 24, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968111
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968112
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968113
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968115
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968116
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968117
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968118
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968119
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 24, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968120
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968121
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968122
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968123
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968124
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968126
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968127
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.z1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968128
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ba1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968129
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bb1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968130
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bc1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968131
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bd1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968132
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.be1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968133
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bf1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968134
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bg1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968135
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bh1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968137
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bi1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.46', 'subgroup_hash': 46, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968138
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bj1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968139
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bk1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968140
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bl1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968141
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bm1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968142
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 24, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bn1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.23', 'subgroup_hash': 23, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60968143
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 12, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bo1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.23', 'subgroup_hash': 23, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60968144
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 24, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bp1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.9', 'subgroup_hash': 9, 'subgroup_order': 48, 'subgroup_tex': 'C_6:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968145
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bq1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.9', 'subgroup_hash': 9, 'subgroup_order': 48, 'subgroup_tex': 'C_6:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968146
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.br1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968149
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bs1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968150
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bt1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968151
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bu1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968152
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bv1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968153
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bw1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968154
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bx1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968155
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.by1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968156
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bz1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968157
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ca1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968158
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cb1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968160
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cc1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968161
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cd1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968162
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ce1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968163
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cf1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968164
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cg1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968165
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ch1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968166
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 16, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ci1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968167
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cj1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968168
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ck1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968169
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cl1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968171
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cm1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968172
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 24, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cn1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968173
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 24, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.co1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968174
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cp1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968175
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cq1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.40', 'subgroup_hash': 40, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968176
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cr1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968177
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.cs1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968178
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ct1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968179
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cu1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968180
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.cv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cv1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60968182
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.cw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cw1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60968183
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.cx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cx1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60968184
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.cy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cy1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60968185
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.cz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cz1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60968186
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.da1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.da1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60968187
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.db1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.db1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60968188
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.dc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dc1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60968189
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.dd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dd1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.6', 'subgroup_hash': 6, 'subgroup_order': 48, 'subgroup_tex': 'C_{24}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60968190
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.de1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.de1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968191
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.de1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.de1.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': 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': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968193
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.df1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.df1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968194
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.df1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.df1.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': 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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968195
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.dg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dg1.a1', 'outer_equivalence': False, 'perfect': False, '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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968196
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.24.dg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dg1.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': 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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968197
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 36, 'counter': 244, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.40', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 40, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times \\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': ['L3', 'C5'], 'split': True, '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: 60968198
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': 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: 60968199
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': 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: 60968200
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.32.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60968201
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.32.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': 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: 60968202
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.32.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': 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: 60968204
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.32.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': 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: 60968205
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.32.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968206
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.32.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 60968207
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.32.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 60968208
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': True, 'core_order': 32, 'counter': 254, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968209
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968210
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968211
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968212
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968213
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968215
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968216
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968217
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968218
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968219
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968220
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968221
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968222
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968223
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968224
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968226
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968227
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968228
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968229
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968230
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968231
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968232
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968233
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968234
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968235
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.z1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968237
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.ba1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968238
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bb1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968239
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bc1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968240
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bd1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968241
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.be1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968242
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bf1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.13', 'subgroup_hash': 13, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968243
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bg1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.13', 'subgroup_hash': 13, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968244
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bh1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968245
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bi1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968246
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bj1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.13', 'subgroup_hash': 13, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968248
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bk1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.13', 'subgroup_hash': 13, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968249
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bl1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968250
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bm1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968251
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 16, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bn1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968252
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bo1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968253
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 16, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bp1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968254
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bq1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968255
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.br1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968256
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bs1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968257
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bt1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.36.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bu1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968261
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 24, 'counter': 301, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60968262
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 24, 'counter': 302, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.36', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 36, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{12}', 'simple': False, 'solvable': True, 'special_labels': ['S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968263
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 24, 'counter': 303, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968264
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': True, 'core_order': 24, 'counter': 304, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1152.155799.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60968265
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 24, 'counter': 305, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968266
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 24, 'counter': 306, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.48.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{24}:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968267
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 24, 'counter': 307, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.48.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{24}:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968268
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968269
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968271
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968272
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 12, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968273
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968274
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60968275
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60968276
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968277
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968278
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968279
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 12, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968280
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968282
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968283
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968284
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968285
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968286
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968287
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968288
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968289
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968290
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968291
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968293
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60968294
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60968295
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60968296
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60968297
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': 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: 60968298
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': 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: 60968299
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': 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: 60968300
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': 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: 60968301
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968302
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968304
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968305
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968306
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968307
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968308
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968309
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968310
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 12, 'counter': 346, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.48.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60968311
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968312
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968313
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968315
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968316
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968317
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968318
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968319
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 8, 'counter': 354, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.48.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60968320
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 355, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.48.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60968321
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968322
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968323
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 8, 'counter': 358, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.48.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ce1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 60968324
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968326
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.cf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cf1.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968327
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968328
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.cg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cg1.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968329
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ch1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968330
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.ch1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ch1.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968331
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ci1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60968332
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.ci1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ci1.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60968333
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968334
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.cj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cj1.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968335
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ck1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60968337
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.ck1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ck1.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60968338
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': 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: 60968339
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': 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: 60968340
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': 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: 60968341
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.cn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cn1.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': 48, 'quotient_simple': 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: 60968342
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.co1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968343
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.co1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.co1.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968344
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': 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: 60968345
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': 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: 60968346
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cr1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': 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: 60968348
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': 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: 60968349
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.48.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ct1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': 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: 60968350
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 64, 'quotient_simple': 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: 60968351
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.64.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.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': 64, 'quotient_simple': 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: 60968352
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.64.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': 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: 60968353
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.64.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.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': 64, 'quotient_simple': 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: 60968354
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.64.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.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': 64, 'quotient_simple': 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: 60968355
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': True, 'core_order': 16, 'counter': 387, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.72.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': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968356
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 60968357
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968359
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968360
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968361
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968362
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968363
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 60968364
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968365
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968366
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968367
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 8, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968368
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968371
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968372
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968373
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968374
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968375
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968376
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968377
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968378
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968379
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968380
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968382
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968383
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968384
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.z1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968385
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ba1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968386
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bb1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968387
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bc1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968388
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bd1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968389
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.be1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968390
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bf1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968391
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bg1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968393
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 8, 'counter': 420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bh1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968394
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 4, 'counter': 421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bi1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968395
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bj1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968396
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bk1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968397
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bl1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968398
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bm1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968399
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bn1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968400
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bo1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968401
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bp1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968402
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bq1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968404
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.br1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968405
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bs1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968406
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bt1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968407
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bu1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968408
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bv1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968409
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bw1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968410
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bx1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968411
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.by1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968412
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bz1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968413
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ca1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968415
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cb1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968416
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cc1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968417
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cd1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968418
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ce1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968419
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cf1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968420
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cg1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968421
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ch1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968422
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ci1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968423
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cj1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968424
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ck1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968426
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cl1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 60968427
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cm1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968428
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.cm1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cm1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968429
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cn1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968430
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.72.cn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cn1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968431
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': True, 'centralizer_order': 192, 'characteristic': True, 'core_order': 12, 'counter': 455, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.187', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 187, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_4:S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968432
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': True, 'core_order': 12, 'counter': 456, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1152.155799.96.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.226', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 226, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60968433
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 12, 'counter': 457, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.96.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '96.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.187', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 187, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_4:S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 60968434
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 12, 'counter': 458, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.96.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.109', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 109, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8:D_6', 'simple': False, 'solvable': True, 'special_labels': ['C6'], '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: 60968435
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 12, 'counter': 459, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.96.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '96.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.120', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 120, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times \\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 60968437
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60968438
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 6, 'counter': 461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60968439
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 6, 'counter': 462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60968440
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60968441
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60968442
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60968443
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60968444
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60968445
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 468, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.96.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60968446
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60968448
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 470, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.96.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60968449
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60968450
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 4, 'counter': 472, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.96.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60968451
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 473, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.96.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60968452
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60968453
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60968454
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 476, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.96.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60968455
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60968456
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60968457
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60968459
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 6, 'counter': 480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60968460
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 6, 'counter': 481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': 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: 60968461
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 6, 'counter': 482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 60968462
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 6, 'counter': 483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.z1.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': 96, 'quotient_simple': 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: 60968463
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 60968464
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ba1.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': 96, 'quotient_simple': 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: 60968465
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 60968466
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 60968467
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bc1.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': 96, 'quotient_simple': 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: 60968468
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 60968470
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 60968471
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 491, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.96.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 60968472
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 60968473
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 60968474
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 60968475
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 60968476
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 60968477
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 497, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.96.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 60968478
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 60968479
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 60968482
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.96.bn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bn1.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': 96, 'quotient_simple': 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: 60968483
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 501, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '1152.155799.128.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.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': 128, 'quotient_simple': 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': 3}
  • id: 60968484
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': True, 'core_order': 8, 'counter': 502, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.144', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 144, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60968485
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': True, 'core_order': 8, 'counter': 503, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1152.155799.144.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.183', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 183, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\times S_4', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968486
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60968487
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60968488
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 4, 'counter': 506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968489
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968490
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968491
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60968493
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60968494
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60968495
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 4, 'counter': 512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968496
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968497
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968498
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968499
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968500
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968501
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968502
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968504
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968505
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968506
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60968507
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968508
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968509
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968510
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968511
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': 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': 0}
  • id: 60968512
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': 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': 0}
  • id: 60968513
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': 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': 0}
  • id: 60968515
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': 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': 0}
  • id: 60968516
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': 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': 0}
  • id: 60968517
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': 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': 0}
  • id: 60968518
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968519
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968520
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 4, 'counter': 535, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968521
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 4, 'counter': 536, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968522
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 537, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968523
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968524
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968526
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968527
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60968528
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60968529
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bo1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bo1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60968530
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60968531
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bp1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60968532
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968533
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bq1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968534
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60968535
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.br1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.br1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60968537
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60968538
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bs1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bs1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 60968539
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968540
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bt1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bt1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968541
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': 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': 0}
  • id: 60968542
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': 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': 0}
  • id: 60968543
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': 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': 0}
  • id: 60968544
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bw1.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': 144, 'quotient_simple': 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': 0}
  • id: 60968545
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': 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': 0}
  • id: 60968546
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bx1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bx1.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': 144, 'quotient_simple': 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': 0}
  • id: 60968548
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': 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': 0}
  • id: 60968549
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.144.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': 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': 0}
  • id: 60968550
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': True, 'core_order': 6, 'counter': 562, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1152.155799.192.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '192.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '192.1470', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1470, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^3:D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60968551
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': True, 'centralizer_order': 192, 'characteristic': False, 'core_order': 6, 'counter': 563, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1152.155799.192.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '192.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '192.960', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 960, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_8:S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60968552
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': True, 'centralizer_order': 192, 'characteristic': False, 'core_order': 6, 'counter': 564, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1152.155799.192.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '192.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '192.960', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 960, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_8:S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 60968553
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 565, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.192.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 60968554
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 566, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.192.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 60968555
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 567, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.192.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 60968556
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 568, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.192.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 60968557
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 3, 'counter': 569, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.192.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 60968559
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 3, 'counter': 570, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.192.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 60968560
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 3, 'counter': 571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.192.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 60968561
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 3, 'counter': 572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.192.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 60968562
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 573, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.192.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 60968563
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.192.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 60968564
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.192.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 60968565
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.192.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 60968566
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.192.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 60968567
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': True, 'core_order': 4, 'counter': 578, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1152.155799.288.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '288.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '288.1028', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1028, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_6\\times S_4', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'U1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60968568
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': True, 'core_order': 4, 'counter': 579, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1152.155799.288.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '288.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '288.440', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 440, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{24}:D_6', 'simple': False, 'solvable': True, 'special_labels': ['D2'], '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: 60968570
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 2, 'counter': 580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.288.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60968571
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 2, 'counter': 581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.288.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60968572
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.288.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60968573
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.288.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60968574
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.288.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60968575
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 585, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.288.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60968576
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 586, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.288.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60968577
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 587, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.288.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60968578
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 588, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.288.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60968579
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 589, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.288.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60968581
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.288.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60968582
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.288.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60968583
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.288.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60968584
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.288.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60968585
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.288.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60968586
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.288.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60968587
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.288.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60968588
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.288.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60968589
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.288.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60968590
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.288.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60968593
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.288.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60968594
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 601, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.288.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60968595
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 602, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.288.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60968596
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.288.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60968597
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.288.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60968598
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.288.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60968599
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 606, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.288.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': 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: 60968600
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 607, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.288.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 60968601
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.288.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 60968602
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1152.155799.288.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.ba1.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': 288, 'quotient_simple': 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: 60968604
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': True, 'core_order': 3, 'counter': 610, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1152.155799.384.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '384.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '384.18014', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 18014, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 384, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^4.D_{12}', 'simple': True, 'solvable': True, 'special_labels': ['C7'], '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: 60968605
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 611, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.384.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.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': 384, '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: 60968606
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 612, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.384.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.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': 384, '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: 60968607
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': True, 'central_factor': False, 'centralizer_order': 1152, 'characteristic': True, 'core_order': 2, 'counter': 613, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1152.155799.576.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '576.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '576.8312', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8312, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 576, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\times C_4:S_4', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U2'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60968608
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 614, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.576.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.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': 576, '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: 60968609
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 615, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.576.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, '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: 60968610
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 616, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.576.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.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': 576, '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: 60968611
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 617, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.576.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.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': 576, '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: 60968612
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 618, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.576.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.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': 576, '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: 60968613
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 619, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.576.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.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': 576, '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: 60968615
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 620, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.576.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.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': 576, '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: 60968616
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 621, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1152.155799.576.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.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': 576, '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: 60968617
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.155799', 'ambient_counter': 155799, 'ambient_order': 1152, 'ambient_tex': 'S_3\\times C_8:S_4', 'central': True, 'central_factor': False, 'centralizer_order': 1152, 'characteristic': True, 'core_order': 1, 'counter': 622, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1152.155799.1152.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1152.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '1152.155799', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7082498570119804226, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1152, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\times C_8:S_4', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U3', 'D3', 'C8'], '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: 60968295
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '48.be1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '24.w1.a1', '24.x1.a1'], 'contains': ['96.h1.a1', '96.n1.a1', '96.o1.a1', '144.x1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4131, -1, 4366, -1, 3790, -1, 5344, -1], 'generators': [577, 120, 48, 384], 'label': '1152.155799.48.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.be1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.be1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968036
    {'ambient': '1152.155799', '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': '576.a1.a1', 'complements': ['1152.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1', '3.a1.a1', '3.b1.a1', '4.j1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4079, 4377, 5427, 6438, 6395, 3834, 3840, 6182], 'generators': [1, 576, 48, 32, 2, 24, 672, 384, 12], 'label': '1152.155799.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '576.8312', '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': '576.8312'}
  • id: 60968037
    {'ambient': '1152.155799', 'aut_centralizer_order': 2, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '768.1083444', 'aut_weyl_index': 6, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.f1.a1', '6.g1.a1', '6.h1.a1', '6.i1.a1', '6.j1.a1', '6.k1.a1', '6.l1.a1', '6.m1.a1', '6.n1.a1', '6.o1.a1', '6.p1.a1', '6.q1.a1', '6.s1.a1', '6.t1.a1', '9.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6296, -1, 6901, -1, 6216, -1, 6719, -1], 'generators': [1, 24, 576, 2, 96, 384, 48, 12], 'label': '1152.155799.3.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': '576.8312', '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': '96.209'}
  • id: 60968038
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '12.bl1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.o1.a1', '6.t1.a1'], 'contains': ['24.bg1.a1', '24.bm1.a1', '24.bn1.a1', '24.cz1.a1', '24.da1.a1', '36.bd1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6979, -1, 8533, -1, 7898, -1, 8064, -1], 'generators': [3, 384, 48, 12, 576, 24], 'label': '1152.155799.12.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bl1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968039
    {'ambient': '1152.155799', 'aut_centralizer_order': 12, 'aut_label': '12.bm1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 36, 'centralizer': '96.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '6.n1.a1', '6.p1.a1'], 'contains': ['24.bh1.a1', '24.bi1.a1', '24.bo1.a1', '36.be1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8463, -1, 7776, -1, 6199, -1, 7545, -1], 'generators': [98, 48, 576, 108, 384, 600], 'label': '1152.155799.12.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bm1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60968040
    {'ambient': '1152.155799', 'aut_centralizer_order': 24, 'aut_label': '12.bn1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '96.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '6.o1.a1', '6.p1.a1'], 'contains': ['24.bh1.a1', '24.bj1.a1', '24.bn1.a1', '36.bf1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6117, -1, 6835, -1, 6410, -1, 6522, -1], 'generators': [98, 48, 576, 12, 384, 24], 'label': '1152.155799.12.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bn1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60968041
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '12.bo1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '6.n1.a1', '6.q1.a1'], 'contains': ['24.bh1.a1', '24.bk1.a1', '24.bp1.a1', '36.bg1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6414, -1, 6714, -1, 5948, -1, 6382, -1], 'generators': [13, 384, 48, 98, 24, 576], 'label': '1152.155799.12.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bo1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968042
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '12.bp1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '6.o1.a1', '6.q1.a1'], 'contains': ['24.bh1.a1', '24.bm1.a1', '24.bq1.a1', '36.bh1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6555, -1, 7843, -1, 6136, -1, 7235, -1], 'generators': [109, 384, 48, 98, 24, 576], 'label': '1152.155799.12.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bp1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968043
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '12.bq1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '6.l1.a1', '6.s1.a1'], 'contains': ['24.bi1.a1', '24.bl1.a1', '24.bq1.a1', '36.bi1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8163, -1, 7254, -1, 6275, -1, 7991, -1], 'generators': [589, 384, 48, 6, 24, 96], 'label': '1152.155799.12.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bq1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968044
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '12.br1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '6.m1.a1', '6.s1.a1'], 'contains': ['24.bj1.a1', '24.bl1.a1', '24.bp1.a1', '36.bj1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6738, -1, 7085, -1, 6080, -1, 6796, -1], 'generators': [13, 384, 48, 582, 24, 96], 'label': '1152.155799.12.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.br1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.br1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968045
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '12.bs1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '6.l1.a1', '6.t1.a1'], 'contains': ['24.bk1.a1', '24.bl1.a1', '24.bn1.a1', '36.bk1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6480, -1, 6771, -1, 5761, -1, 6231, -1], 'generators': [99, 384, 48, 12, 24, 576], 'label': '1152.155799.12.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bs1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968046
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '12.bt1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '6.m1.a1', '6.t1.a1'], 'contains': ['24.bl1.a1', '24.bm1.a1', '24.bo1.a1', '36.bl1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7634, -1, 7724, -1, 5696, -1, 7689, -1], 'generators': [99, 384, 48, 108, 600, 576], 'label': '1152.155799.12.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bt1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968047
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '12.bu1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '6.j1.a1'], 'contains': ['24.d1.a1', '24.ba1.a1', '24.bc1.a1', '24.bf1.a1', '24.bt1.a1', '24.by1.a1', '24.ca1.a1', '36.bm1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2565, -1, 3289, -1, 1865, -1, 2391, -1], 'generators': [25, 384, 576, 2, 96, 48], 'label': '1152.155799.12.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '12.bu1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60968048
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 8, 'centralizer': '144.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '12.a1.a1', '12.h1.a1', '16.d1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3015, 897, 3563, 3265, 4074, 614, 3060, 2253], 'generators': [1, 576, 672, 24, 384, 32, 48], 'label': '1152.155799.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '576.8312', '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': '144.183'}
  • id: 60968049
    {'ambient': '1152.155799', 'aut_centralizer_order': 24, 'aut_label': '12.bv1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '96.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.j1.a1', '6.p1.a1', '6.q1.a1'], 'contains': ['24.c1.a1', '24.bb1.a1', '24.bd1.a1', '24.bh1.a1', '24.by1.a1', '36.bn1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4984, -1, 5218, -1, 4347, -1, 4857, -1], 'generators': [2, 576, 48, 24, 96, 384], 'label': '1152.155799.12.bv1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bv1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60968050
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '12.bw1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '6.c1.a1'], 'contains': ['24.bz1.a1', '24.cb1.a1', '24.cf1.a1', '36.bm1.a1', '48.bk1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1125, -1, 1786, -1, 2011, -1, 2173, -1], 'generators': [25, 576, 672, 2, 48, 32], 'label': '1152.155799.12.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.bw1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 60968051
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '12.bx1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.j1.a1', '6.s1.a1', '6.t1.a1'], 'contains': ['24.c1.a1', '24.be1.a1', '24.bg1.a1', '24.bl1.a1', '24.ca1.a1', '36.bo1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4294, -1, 5472, -1, 3996, -1, 4780, -1], 'generators': [3, 384, 576, 24, 96, 48], 'label': '1152.155799.12.bx1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bx1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968052
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '12.by1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 24, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.c1.a1', '6.u1.a1', '6.v1.a1'], 'contains': ['24.e1.a1', '24.cb1.a1', '36.bo1.a1', '48.bo1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3368, -1, 4197, -1, 5019, -1, 3329, -1], 'generators': [3, 576, 672, 24, 48, 32], 'label': '1152.155799.12.by1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.by1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.by1.a1', 'subgroup_fusion': None, 'weyl_group': '96.187'}
  • id: 60968053
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '12.bz1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 24, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.w1.a1'], 'contains': ['24.cc1.a1', '24.ci1.a1', '36.bo1.a1', '48.bp1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4071, -1, 5079, -1, 3835, -1, 4025, -1], 'generators': [3, 576, 672, 24, 48, 416], 'label': '1152.155799.12.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1.a1', 'old_label': '12.bz1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '96.187'}
  • id: 60968054
    {'ambient': '1152.155799', 'aut_centralizer_order': 24, 'aut_label': '12.ca1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '96.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.k1.a1', '6.p1.a1', '6.s1.a1'], 'contains': ['24.c1.a1', '24.bi1.a1', '24.bj1.a1', '24.br1.a1', '24.cd1.a1', '36.bp1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5366, -1, 6389, -1, 5199, -1, 5864, -1], 'generators': [6, 96, 48, 24, 576, 384], 'label': '1152.155799.12.ca1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.ca1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60968055
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '12.cb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.k1.a1', '6.q1.a1', '6.t1.a1'], 'contains': ['24.c1.a1', '24.bk1.a1', '24.bm1.a1', '24.bs1.a1', '24.ce1.a1', '36.bq1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5083, -1, 5410, -1, 4587, -1, 5721, -1], 'generators': [7, 384, 96, 24, 576, 48], 'label': '1152.155799.12.cb1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.cb1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968056
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '12.cc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '6.k1.a1'], 'contains': ['24.d1.a1', '24.bu1.a1', '24.bv1.a1', '24.bw1.a1', '24.bx1.a1', '24.cd1.a1', '24.ce1.a1', '36.bs1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3607, -1, 4316, -1, 3193, -1, 5170, -1], 'generators': [25, 384, 96, 6, 576, 48], 'label': '1152.155799.12.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '12.cc1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60968057
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '12.cd1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 24, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.d1.a1', '6.r1.a1', '6.v1.a1'], 'contains': ['24.e1.a1', '24.ch1.a1', '36.bq1.a1', '48.bz1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3676, -1, 3573, -1, 5453, -1, 3368, -1], 'generators': [7, 576, 96, 24, 48, 32], 'label': '1152.155799.12.cd1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.cd1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '96.187'}
  • id: 60968058
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '12.ce1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '72.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.e1.a1', '6.r1.a1', '6.u1.a1'], 'contains': ['24.e1.a1', '36.br1.a1', '48.cb1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5156, -1, 5572, -1, 9295, -1, 4350, -1], 'generators': [13, 576, 96, 32, 24, 48], 'label': '1152.155799.12.ce1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.ce1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60968059
    {'ambient': '1152.155799', 'aut_centralizer_order': 12, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '384.20051', 'aut_weyl_index': 12, 'centralizer': '192.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.b1.a1', '8.g1.a1', '12.b1.a1', '12.bv1.a1', '16.g1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3287, 5408, 4674, 8560, 4420, 4798, 3357, 7816], 'generators': [2, 672, 32, 24, 576, 384, 48], 'label': '1152.155799.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.b1.a1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '192.1470'}
  • id: 60968367
    {'ambient': '1152.155799', 'aut_centralizer_order': 192, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.i1.a1', '36.g1.a1', '36.m1.a1'], 'contains': ['144.b1.a1', '144.e1.a1', '144.bi1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6059, -1, 6676, -1, 9016, -1, 8419, -1], 'generators': [1, 12], 'label': '1152.155799.72.l1.a1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.l1.a1', 'projective_image': '576.8312', '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': '2.1'}
  • id: 60968060
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '12.cf1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '6.d1.a1'], 'contains': ['24.cf1.a1', '24.cg1.a1', '24.ch1.a1', '36.bs1.a1', '48.cc1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1831, -1, 2101, -1, 3506, -1, 3113, -1], 'generators': [25, 576, 96, 6, 48, 32], 'label': '1152.155799.12.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.cf1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 60968061
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '12.cg1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 24, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.w1.a1'], 'contains': ['24.ci1.a1', '24.cj1.a1', '36.bq1.a1', '48.cd1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4711, -1, 4976, -1, 4408, -1, 4143, -1], 'generators': [7, 576, 96, 24, 48, 416], 'label': '1152.155799.12.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1.a1', 'old_label': '12.cg1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '96.187'}
  • id: 60968062
    {'ambient': '1152.155799', 'aut_centralizer_order': 24, 'aut_label': '12.ch1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.w1.a1'], 'contains': ['24.ci1.a1', '36.a1.a1', '48.ce1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5256, -1, 5861, -1, 6476, -1, 4926, -1], 'generators': [12, 576, 96, 416, 24, 48], 'label': '1152.155799.12.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '12.ch1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60968063
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '12.ci1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1'], 'contains': ['24.ck1.a1', '24.cm1.a1', '24.cn1.a1', '24.cr1.a1', '24.cu1.a1', '24.cy1.a1', '24.cz1.a1', '36.bt1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9261, -1, 9495, -1, 8522, -1, 8842, -1], 'generators': [577, 384, 48, 2, 12, 24], 'label': '1152.155799.12.ci1.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': '12.ci1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60968064
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '12.cj1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1'], 'contains': ['24.ck1.a1', '24.cm1.a1', '24.co1.a1', '24.cs1.a1', '24.ct1.a1', '24.cx1.a1', '24.da1.a1', '36.bu1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9472, -1, 9245, -1, 8706, -1, 9038, -1], 'generators': [577, 384, 48, 2, 588, 24], 'label': '1152.155799.12.cj1.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': '12.cj1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60968065
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '16.a1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '48.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.g1.a1', '8.h1.a1', '8.i1.a1', '8.j1.a1'], 'contains': ['32.a1.a1', '48.b1.a1', '48.c1.a1', '48.ba1.a1', '64.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [627, 1799, 1042, 2641, 992, 1989, 1508, 2561], 'generators': [48, 576, 32, 384, 672], 'label': '1152.155799.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'normal_contains': ['32.a1.a1', '48.b1.a1', '48.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 60968066
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '16.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '144.183', 'aut_weyl_index': 32, 'centralizer': '144.b1.a1', 'complements': ['72.ce1.a1', '72.cf1.a1', '72.ck1.a1', '72.cl1.a1', '72.cg1.a1', '72.ch1.a1', '72.ci1.a1', '72.cj1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.o1.a1'], 'contains': ['32.a1.a1', '48.f1.a1', '48.cf1.a1', '64.b1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [281, 669, 227, 742, 485, 1121, 419, 1845], 'generators': [1, 384, 32, 672, 576], 'label': '1152.155799.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.a1.a1', '48.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '1152.155799', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 60968067
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '16.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '144.183', 'aut_weyl_index': 32, 'centralizer': '144.b1.a1', 'complements': ['72.ce1.a1', '72.cf1.a1', '72.ck1.a1', '72.cl1.a1', '72.cg1.a1', '72.ch1.a1', '72.ci1.a1', '72.cj1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.o1.b1'], 'contains': ['32.a1.a1', '48.f1.b1', '48.cf1.b1', '64.b1.b1'], 'core': '16.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [281, 669, 347, 1570, 485, 1121, 176, 1135], 'generators': [49, 384, 32, 672, 576], 'label': '1152.155799.16.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.b1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.a1.a1', '48.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.b1', 'projective_image': '1152.155799', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.b1.b1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 60968068
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '144.192', 'aut_weyl_index': 32, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '8.d1.a1'], 'contains': ['32.b1.a1', '32.c1.a1', '32.d1.a1', '32.i1.a1', '32.i1.b1', '48.g1.a1', '48.k1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [921, -1, 1301, -1, 2244, -1, 1300, -1], 'generators': [1, 384, 2, 48, 32], 'label': '1152.155799.16.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.d1.a1', 'old_label': '16.c1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 60968069
    {'ambient': '1152.155799', 'aut_centralizer_order': 24, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '48.ca1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '8.d1.a1', '8.e1.a1', '8.f1.a1'], 'contains': ['32.b1.a1', '32.e1.a1', '32.f1.a1', '48.a1.a1', '48.h1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2099, -1, 3445, -1, 5250, -1, 2819, -1], 'generators': [1, 384, 24, 32, 48], 'label': '1152.155799.16.d1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.d1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968070
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '1152.157559', 'aut_weyl_index': 4, 'centralizer': '576.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.h1.a1', '12.bx1.a1', '12.by1.a1', '12.bz1.a1', '16.h1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3876, 2034, 5032, 5548, 4146, 1668, 3433, 7057], 'generators': [3, 672, 384, 24, 576, 48, 32], 'label': '1152.155799.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '576.8312'}
  • id: 60968071
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '144.192', 'aut_weyl_index': 32, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '8.e1.a1'], 'contains': ['32.b1.a1', '32.g1.a1', '32.h1.a1', '48.i1.a1', '48.m1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1780, -1, 2232, -1, 3919, -1, 3116, -1], 'generators': [1, 384, 6, 48, 32], 'label': '1152.155799.16.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1.a1', 'old_label': '16.e1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 60968072
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '144.192', 'aut_weyl_index': 32, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '8.d1.a1'], 'contains': ['32.c1.a1', '32.d1.a1', '32.f1.a1', '48.bg1.a1', '48.bk1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1185, -1, 1766, -1, 2592, -1, 2125, -1], 'generators': [25, 384, 2, 48, 32], 'label': '1152.155799.16.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.d1.a1', 'old_label': '16.f1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 60968073
    {'ambient': '1152.155799', 'aut_centralizer_order': 12, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '8.d1.a1', '8.k1.a1', '8.l1.a1'], 'contains': ['32.c1.a1', '32.e1.a1', '48.bi1.a1', '48.bl1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2710, -1, 4481, -1, 5784, -1, 3250, -1], 'generators': [2, 32, 24, 384, 48], 'label': '1152.155799.16.g1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.g1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1.a1', 'subgroup_fusion': None, 'weyl_group': '48.36'}
  • id: 60968074
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '288.958', 'aut_weyl_index': 16, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '8.d1.a1', '8.m1.a1', '8.n1.a1'], 'contains': ['32.d1.a1', '32.e1.a1', '48.bm1.a1', '48.bo1.a1', '48.bp1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3619, -1, 5225, -1, 5648, -1, 3454, -1], 'generators': [3, 384, 24, 48, 32], 'label': '1152.155799.16.h1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.h1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.a1', 'subgroup_fusion': None, 'weyl_group': '144.144'}
  • id: 60968075
    {'ambient': '1152.155799', 'aut_centralizer_order': 12, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '8.e1.a1', '8.k1.a1', '8.m1.a1'], 'contains': ['32.e1.a1', '32.g1.a1', '48.bq1.a1', '48.by1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2775, -1, 5278, -1, 8824, -1, 3635, -1], 'generators': [6, 32, 24, 384, 48], 'label': '1152.155799.16.i1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.i1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.a1', 'subgroup_fusion': None, 'weyl_group': '48.36'}
  • id: 60968076
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '288.958', 'aut_weyl_index': 16, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '8.e1.a1', '8.l1.a1', '8.n1.a1'], 'contains': ['32.e1.a1', '32.h1.a1', '48.br1.a1', '48.bz1.a1', '48.cd1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4014, -1, 4604, -1, 6511, -1, 3558, -1], 'generators': [7, 384, 24, 48, 32], 'label': '1152.155799.16.j1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.j1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.a1', 'subgroup_fusion': None, 'weyl_group': '144.144'}
  • id: 60968077
    {'ambient': '1152.155799', 'aut_centralizer_order': 72, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '8.f1.a1', '8.k1.a1', '8.n1.a1'], 'contains': ['32.e1.a1', '48.d1.a1', '48.ca1.a1', '48.ce1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4190, -1, 5964, -1, 9549, -1, 4187, -1], 'generators': [12, 48, 32, 384, 24], 'label': '1152.155799.16.k1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.k1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968078
    {'ambient': '1152.155799', 'aut_centralizer_order': 24, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '48.ca1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '8.f1.a1', '8.l1.a1', '8.m1.a1'], 'contains': ['32.e1.a1', '48.e1.a1', '48.cb1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4528, -1, 5706, -1, 9775, -1, 4257, -1], 'generators': [13, 384, 32, 24, 48], 'label': '1152.155799.16.l1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.l1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968079
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '144.192', 'aut_weyl_index': 32, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '8.e1.a1'], 'contains': ['32.f1.a1', '32.g1.a1', '32.h1.a1', '48.bw1.a1', '48.cc1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2154, -1, 2360, -1, 3997, -1, 3175, -1], 'generators': [25, 384, 6, 48, 32], 'label': '1152.155799.16.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1.a1', 'old_label': '16.m1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 60968080
    {'ambient': '1152.155799', 'aut_centralizer_order': 24, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.o1.a1', '8.o1.b1'], 'contains': ['32.a1.a1', '48.cp1.a1', '48.cq1.a1', '64.c1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [129, -1, 177, -1, 263, -1, 289, -1], 'generators': [2, 576, 384, 32, 672], 'label': '1152.155799.16.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.n1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.n1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 60968081
    {'ambient': '1152.155799', 'aut_centralizer_order': 12, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '384.20051', 'aut_weyl_index': 12, 'centralizer': '192.a1.a1', 'complements': ['288.o1.a1', '288.ba1.a1', '288.o1.b1', '288.ba1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'contains': ['8.b1.a1', '8.i1.a1', '12.e1.a1', '12.ca1.a1', '16.i1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3374, 4251, 5328, 6432, 5473, 3724, 3569, 6299], 'generators': [6, 96, 32, 24, 576, 384, 48], 'label': '1152.155799.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'normal_contains': ['8.b1.a1', '12.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '576.8312', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '192.1470'}
  • id: 60968082
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '16.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '144.183', 'aut_weyl_index': 32, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.o1.a1', '8.o1.b1'], 'contains': ['32.a1.a1', '48.cr1.a1', '48.cs1.a1', '48.ct1.a1', '64.d1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [186, -1, 134, -1, 171, -1, 224, -1], 'generators': [3, 576, 32, 384, 672], 'label': '1152.155799.16.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.o1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.o1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 60968083
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '9.a1.a1'], 'contains': ['36.c1.a1', '36.e1.a1', '36.g1.a1', '36.m1.a1', '36.n1.a1', '36.w1.a1', '36.z1.a1', '36.ba1.a1', '36.bd1.a1', '36.bt1.a1', '36.bu1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8219, -1, 8276, -1, 8825, -1, 8940, -1], 'generators': [1, 2, 12, 576], 'label': '1152.155799.18.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968084
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 36, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '9.a1.a1'], 'contains': ['36.c1.a1', '36.f1.a1', '36.h1.a1', '36.x1.a1', '36.y1.a1', '36.bb1.a1', '36.bc1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6475, -1, 6792, -1, 6710, -1, 6859, -1], 'generators': [1, 2, 108], 'label': '1152.155799.18.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': '18.b1.a1', 'projective_image': '576.8312', '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': '16.11'}
  • id: 60968085
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 36, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '9.a1.a1'], 'contains': ['36.d1.a1', '36.e1.a1', '36.h1.a1', '36.be1.a1', '36.bh1.a1', '36.bi1.a1', '36.bl1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7971, -1, 7877, -1, 6857, -1, 7918, -1], 'generators': [1, 98, 108], 'label': '1152.155799.18.c1.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.c1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968086
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '9.a1.a1'], 'contains': ['36.d1.a1', '36.f1.a1', '36.g1.a1', '36.bf1.a1', '36.bg1.a1', '36.bj1.a1', '36.bk1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5828, -1, 6289, -1, 6784, -1, 6649, -1], 'generators': [1, 98, 12], 'label': '1152.155799.18.d1.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.d1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968087
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.j1.a1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.c1.a1', '36.d1.a1', '36.j1.a1', '36.k1.a1', '36.o1.a1', '36.p1.a1', '36.q1.a1', '36.bm1.a1', '36.bn1.a1', '36.bo1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3983, -1, 4117, -1, 4511, -1, 4084, -1], 'generators': [1, 2, 24, 96], 'label': '1152.155799.18.e1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.e1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968088
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.k1.a1', '9.a1.a1'], 'contains': ['36.e1.a1', '36.f1.a1', '36.i1.a1', '36.k1.a1', '36.l1.a1', '36.r1.a1', '36.s1.a1', '36.v1.a1', '36.bp1.a1', '36.bq1.a1', '36.bs1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5144, -1, 5125, -1, 5282, -1, 5944, -1], 'generators': [1, 6, 24, 576], 'label': '1152.155799.18.f1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.f1.a1', 'projective_image': '576.8312', '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': '16.11'}
  • id: 60968089
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.e1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.g1.a1', '36.h1.a1', '36.k1.a1', '36.t1.a1', '36.u1.a1', '36.br1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6049, -1, 6349, -1, 8250, -1, 8496, -1], 'generators': [1, 12, 96, 576], 'label': '1152.155799.18.g1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.g1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968090
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 36, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.l1.a1', '9.a1.a1'], 'contains': ['36.p1.a1', '36.r1.a1', '36.t1.a1', '36.w1.a1', '36.y1.a1', '36.bi1.a1', '36.bk1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6960, -1, 6725, -1, 7466, -1, 7301, -1], 'generators': [97, 2, 12], 'label': '1152.155799.18.h1.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.h1.a1', 'projective_image': '576.8312', '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': '16.11'}
  • id: 60968091
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 36, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.m1.a1', '9.a1.a1'], 'contains': ['36.p1.a1', '36.s1.a1', '36.u1.a1', '36.x1.a1', '36.z1.a1', '36.bj1.a1', '36.bl1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6548, -1, 7084, -1, 7030, -1, 7622, -1], 'generators': [97, 2, 108], 'label': '1152.155799.18.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': '18.i1.a1', 'projective_image': '576.8312', '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': '16.11'}
  • id: 60968092
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '1152.157559', 'aut_weyl_index': 4, 'centralizer': '576.a1.a1', 'complements': ['288.o1.a1', '288.ba1.a1', '288.o1.b1', '288.ba1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.j1.a1', '12.cb1.a1', '12.cd1.a1', '12.cg1.a1', '16.j1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4179, 3060, 4755, 7496, 5018, 2619, 3496, 5387], 'generators': [7, 96, 384, 24, 576, 48, 32], 'label': '1152.155799.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '576.8312', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '576.8312'}
  • id: 60968093
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '18.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 36, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.n1.a1', '9.a1.a1'], 'contains': ['36.q1.a1', '36.r1.a1', '36.u1.a1', '36.ba1.a1', '36.bc1.a1', '36.be1.a1', '36.bg1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7385, -1, 7200, -1, 7379, -1, 7385, -1], 'generators': [97, 98, 108], 'label': '1152.155799.18.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': '576.8312', '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': '16.11'}
  • id: 60968094
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '18.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 36, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.o1.a1', '9.a1.a1'], 'contains': ['36.q1.a1', '36.s1.a1', '36.t1.a1', '36.bb1.a1', '36.bd1.a1', '36.bf1.a1', '36.bh1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5978, -1, 7273, -1, 7726, -1, 7468, -1], 'generators': [97, 98, 12], 'label': '1152.155799.18.k1.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.k1.a1', 'projective_image': '576.8312', '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': '16.11'}
  • id: 60968095
    {'ambient': '1152.155799', 'aut_centralizer_order': 24, 'aut_label': '18.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.p1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.w1.a1', '36.x1.a1', '36.be1.a1', '36.bf1.a1', '36.bn1.a1', '36.bp1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5616, -1, 6119, -1, 7639, -1, 7006, -1], 'generators': [2, 12, 96], 'label': '1152.155799.18.l1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.l1.a1', 'projective_image': '576.8312', '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': '16.11'}
  • id: 60968096
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '18.m1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.q1.a1', '6.r1.a1', '9.a1.a1'], 'contains': ['36.y1.a1', '36.z1.a1', '36.bg1.a1', '36.bh1.a1', '36.bn1.a1', '36.bq1.a1', '36.br1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5710, -1, 5931, -1, 7292, -1, 6726, -1], 'generators': [13, 2, 96], 'label': '1152.155799.18.m1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.m1.a1', 'projective_image': '576.8312', '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': '16.11'}
  • id: 60968097
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '18.n1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.s1.a1', '6.u1.a1', '9.a1.a1'], 'contains': ['36.ba1.a1', '36.bb1.a1', '36.bi1.a1', '36.bj1.a1', '36.bo1.a1', '36.bp1.a1', '36.br1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5900, -1, 6192, -1, 7552, -1, 7090, -1], 'generators': [13, 6, 576], 'label': '1152.155799.18.n1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.n1.a1', 'projective_image': '576.8312', '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': '16.11'}
  • id: 60968098
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '18.o1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.t1.a1', '6.v1.a1', '6.w1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.bc1.a1', '36.bd1.a1', '36.bk1.a1', '36.bl1.a1', '36.bo1.a1', '36.bq1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5522, -1, 6004, -1, 6631, -1, 6152, -1], 'generators': [3, 12, 96], 'label': '1152.155799.18.o1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.o1.a1', 'projective_image': '576.8312', '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': '16.11'}
  • id: 60968099
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '24.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '72.46', 'aut_weyl_index': 64, 'centralizer': '36.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.s1.a1', '12.t1.a1'], 'contains': ['48.b1.a1', '48.f1.a1', '48.f1.b1', '48.j1.a1', '48.n1.a1', '48.cg1.a1', '48.cg1.b1', '72.h1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1763, 2734, 2168, 2171, 1262, 2927, 1823, 366], 'generators': [1, 384, 48, 96, 576], 'label': '1152.155799.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1'], 'normal_contains': ['48.b1.a1', '48.f1.b1', '48.f1.a1', '96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 60968100
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '24.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '12.f1.a1', 'complements': ['48.cq1.a1', '48.cs1.a1', '48.ct1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.p1.a1', '12.u1.a1'], 'contains': ['48.a1.a1', '48.d1.a1', '48.e1.a1', '72.l1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6211, 8874, 7667, 4941, 9484, 8634, 8585, 4480], 'generators': [1, 384, 12, 24, 48], 'label': '1152.155799.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['48.a1.a1', '48.d1.a1', '48.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '576.8312', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.3', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968101
    {'ambient': '1152.155799', 'aut_centralizer_order': 192, 'aut_label': '24.c1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '12.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.a1.a1', '12.c1.a1', '12.d1.a1', '12.bv1.a1', '12.bx1.a1', '12.ca1.a1', '12.cb1.a1'], 'contains': ['48.b1.a1', '48.q1.a1', '48.r1.a1', '72.a1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5331, 6157, 5518, 6166, 4155, 6346, 5003, 5530], 'generators': [24, 48, 96, 576, 384], 'label': '1152.155799.24.c1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.c1.a1', 'normal_contained_in': ['8.b1.a1', '12.a1.a1', '12.c1.a1', '12.d1.a1'], 'normal_contains': ['48.b1.a1', '72.a1.a1', '96.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '576.8312', 'quotient_action_image': '12.4', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968102
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '24.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '72.46', 'aut_weyl_index': 64, 'centralizer': '36.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.a1.a1', '12.bu1.a1', '12.cc1.a1'], 'contains': ['48.b1.a1', '48.s1.a1', '48.t1.a1', '72.bu1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2298, 4869, 3088, 3704, 2319, 4033, 4348, 3420], 'generators': [25, 384, 96, 576, 48], 'label': '1152.155799.24.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.d1.a1', 'normal_contained_in': ['8.c1.a1', '12.a1.a1'], 'normal_contains': ['48.b1.a1', '96.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '576.8312', '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': '36.10'}
  • id: 60968103
    {'ambient': '1152.155799', 'aut_centralizer_order': 24, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '192.1537', 'aut_weyl_index': 24, 'centralizer': '48.d1.a1', 'complements': ['288.o1.a1', '288.ba1.a1', '288.o1.b1', '288.ba1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '12.c1.a1', '12.f1.a1', '12.ch1.a1', '16.k1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4368, 7959, 5820, 9574, 7036, 8050, 4329, 8685], 'generators': [12, 672, 48, 32, 576, 384, 24], 'label': '1152.155799.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1', '12.c1.a1', '12.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '576.8312', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 60968104
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '24.e1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.b1.a1', '12.e1.a1', '12.f1.a1', '12.h1.a1', '12.by1.a1', '12.cd1.a1', '12.ce1.a1'], 'contains': ['48.c1.a1', '72.a1.a1', '96.r1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3451, 3745, 4289, 7544, 5866, 5074, 3329, 6787], 'generators': [24, 576, 32, 48, 96], 'label': '1152.155799.24.e1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.e1.a1', 'normal_contained_in': ['8.b1.a1', '12.b1.a1', '12.e1.a1', '12.f1.a1'], 'normal_contains': ['48.c1.a1', '72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.e1.a1', 'projective_image': '576.8312', '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': '24.12'}
  • id: 60968105
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '72.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.g1.a1', '12.h1.a1', '12.i1.a1'], 'contains': ['48.c1.a1', '48.cf1.a1', '48.cf1.b1', '72.h1.a1', '96.f1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1012, -1, 751, -1, 1612, -1, 1234, -1], 'generators': [1, 576, 48, 32, 96], 'label': '1152.155799.24.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.f1.a1', 'projective_image': '576.8312', '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': '24.12'}
  • id: 60968106
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '8.d1.a1', '12.j1.a1'], 'contains': ['48.g1.a1', '48.h1.a1', '48.bk1.a1', '48.bl1.a1', '48.bo1.a1', '72.i1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1918, -1, 2595, -1, 5452, -1, 2750, -1], 'generators': [1, 32, 2, 24, 48], 'label': '1152.155799.24.g1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '24.g1.a1', 'projective_image': '576.8312', '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': '24.6'}
  • id: 60968107
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '8.e1.a1', '12.j1.a1'], 'contains': ['48.h1.a1', '48.i1.a1', '48.by1.a1', '48.bz1.a1', '48.cc1.a1', '72.k1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2183, -1, 3867, -1, 6820, -1, 3393, -1], 'generators': [1, 32, 6, 24, 48], 'label': '1152.155799.24.h1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '24.h1.a1', 'projective_image': '576.8312', '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': '24.6'}
  • id: 60968108
    {'ambient': '1152.155799', 'aut_centralizer_order': 24, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '24.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '8.f1.a1', '12.j1.a1'], 'contains': ['48.h1.a1', '48.ca1.a1', '48.cb1.a1', '72.l1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4600, -1, 5779, -1, 9968, -1, 4118, -1], 'generators': [1, 48, 12, 32, 24], 'label': '1152.155799.24.i1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '24.i1.a1', 'projective_image': '576.8312', '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': '2.1'}
  • id: 60968109
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.l1.a1', '12.s1.a1'], 'contains': ['48.j1.a1', '48.k1.a1', '48.o1.a1', '48.p1.a1', '48.bb1.a1', '48.ch1.a1', '48.ch1.b1', '48.cj1.a1', '48.cj1.b1', '72.b1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2946, -1, 3411, -1, 1681, -1, 2220, -1], 'generators': [1, 384, 2, 48, 576], 'label': '1152.155799.24.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '24.j1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60968110
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.l1.a1', '12.m1.a1', '12.n1.a1', '12.o1.a1', '12.p1.a1', '12.q1.a1'], 'contains': ['48.a1.a1', '48.j1.a1', '48.l1.a1', '48.q1.a1', '48.s1.a1', '48.bc1.a1', '48.bd1.a1', '72.c1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7742, -1, 8112, -1, 4448, -1, 6414, -1], 'generators': [1, 384, 24, 96, 48], 'label': '1152.155799.24.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.k1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968111
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.k1.a1', '12.r1.a1'], 'contains': ['48.j1.a1', '48.l1.a1', '48.r1.a1', '48.t1.a1', '48.be1.a1', '72.d1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3956, -1, 3937, -1, 2889, -1, 4624, -1], 'generators': [1, 384, 600, 96, 48], 'label': '1152.155799.24.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.l1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968112
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '144.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.m1.a1', '12.s1.a1'], 'contains': ['48.j1.a1', '48.u1.a1', '48.y1.a1', '48.ci1.a1', '48.ci1.b1', '72.e1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2576, -1, 3295, -1, 1531, -1, 1916, -1], 'generators': [1, 384, 98, 48, 576], 'label': '1152.155799.24.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '24.m1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60968113
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '144.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '12.r1.a1', '12.t1.a1'], 'contains': ['48.j1.a1', '48.m1.a1', '48.v1.a1', '48.z1.a1', '48.bf1.a1', '72.f1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5102, -1, 4910, -1, 3762, -1, 6107, -1], 'generators': [1, 384, 6, 96, 48], 'label': '1152.155799.24.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '24.n1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60968114
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 8, 'centralizer': '144.b1.a1', 'complements': ['288.o1.a1', '288.ba1.a1', '288.o1.b1', '288.ba1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'contains': ['8.b1.a1', '12.d1.a1', '12.ce1.a1', '16.l1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4547, 6560, 5666, 4663, 7322, 5865, 4414, 4475], 'generators': [13, 576, 672, 32, 384, 24, 48], 'label': '1152.155799.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'normal_contains': ['8.b1.a1', '12.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '576.8312', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 60968115
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '144.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '12.r1.a1', '12.t1.a1'], 'contains': ['48.j1.a1', '48.w1.a1', '48.x1.a1', '48.ck1.a1', '48.ck1.b1', '72.g1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4720, -1, 4540, -1, 2704, -1, 4471, -1], 'generators': [1, 384, 582, 96, 144], 'label': '1152.155799.24.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '24.o1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60968116
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.l1.a1', '12.u1.a1', '12.v1.a1'], 'contains': ['48.a1.a1', '48.k1.a1', '48.bg1.a1', '48.bi1.a1', '48.bm1.a1', '72.i1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6943, -1, 7519, -1, 5592, -1, 6822, -1], 'generators': [1, 384, 2, 24, 48], 'label': '1152.155799.24.p1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.p1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60968117
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1'], 'contains': ['48.k1.a1', '48.l1.a1', '48.bh1.a1', '48.bj1.a1', '48.bn1.a1', '72.j1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7613, -1, 7955, -1, 4355, -1, 4000, -1], 'generators': [1, 384, 2, 600, 48], 'label': '1152.155799.24.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '24.q1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.q1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60968118
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.n1.a1', '12.u1.a1', '12.v1.a1'], 'contains': ['48.a1.a1', '48.m1.a1', '48.bq1.a1', '48.br1.a1', '48.bw1.a1', '72.k1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9304, -1, 9074, -1, 6455, -1, 7988, -1], 'generators': [1, 384, 6, 24, 48], 'label': '1152.155799.24.r1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.r1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60968119
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.a1', '12.q1.a1', '12.v1.a1'], 'contains': ['48.a1.a1', '48.bs1.a1', '48.bt1.a1', '72.m1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9006, -1, 9845, -1, 7747, -1, 9882, -1], 'generators': [1, 384, 108, 24, 48], 'label': '1152.155799.24.s1.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': '24.s1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968120
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1'], 'contains': ['48.l1.a1', '48.m1.a1', '48.bu1.a1', '48.bv1.a1', '48.bx1.a1', '72.n1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9989, -1, 9292, -1, 5062, -1, 7373, -1], 'generators': [1, 384, 6, 120, 48], 'label': '1152.155799.24.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '24.t1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60968121
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1.a1', '12.w1.a1', '12.x1.a1'], 'contains': ['48.n1.a1', '48.o1.a1', '48.y1.a1', '48.cn1.a1', '48.cn1.b1', '72.o1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2501, -1, 2841, -1, 1119, -1, 2065, -1], 'generators': [97, 384, 2, 48, 576], 'label': '1152.155799.24.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '24.u1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60968122
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1.a1', '12.w1.a1', '12.y1.a1'], 'contains': ['48.n1.a1', '48.p1.a1', '48.u1.a1', '48.co1.a1', '48.co1.b1', '72.p1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2435, -1, 2780, -1, 1192, -1, 1995, -1], 'generators': [97, 384, 98, 48, 576], 'label': '1152.155799.24.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '24.v1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.v1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60968123
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '24.w1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.x1.a1', '12.y1.a1', '12.z1.a1', '12.ba1.a1', '12.bb1.a1', '12.bc1.a1'], 'contains': ['48.n1.a1', '48.q1.a1', '48.t1.a1', '48.bc1.a1', '48.be1.a1', '72.q1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8053, -1, 8397, -1, 4802, -1, 6325, -1], 'generators': [577, 384, 24, 96, 48], 'label': '1152.155799.24.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.w1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.w1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968124
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.w1.a1', '12.bd1.a1'], 'contains': ['48.n1.a1', '48.r1.a1', '48.s1.a1', '48.bd1.a1', '48.be1.a1', '72.r1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3827, -1, 3783, -1, 2796, -1, 4713, -1], 'generators': [577, 384, 600, 96, 48], 'label': '1152.155799.24.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.x1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.x1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968125
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 8, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.g1.a1', '8.h1.a1', '8.o1.a1', '8.o1.b1', '12.g1.a1', '12.s1.a1', '16.c1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1042, -1, 1001, -1, 1435, -1, 1426, -1], 'generators': [1, 672, 384, 2, 576, 48, 32], 'label': '1152.155799.4.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': '4.h1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 60968126
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1.a1', '12.z1.a1', '12.bd1.a1'], 'contains': ['48.n1.a1', '48.v1.a1', '48.x1.a1', '72.s1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4286, -1, 4387, -1, 3078, -1, 5167, -1], 'generators': [577, 384, 6, 48, 96], 'label': '1152.155799.24.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '24.y1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.y1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60968127
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1.a1', '12.ba1.a1', '12.bd1.a1'], 'contains': ['48.n1.a1', '48.w1.a1', '48.z1.a1', '72.t1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4359, -1, 4470, -1, 3038, -1, 5206, -1], 'generators': [577, 384, 582, 144, 96], 'label': '1152.155799.24.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '24.z1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.z1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60968128
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '12.w1.a1', '12.bu1.a1'], 'contains': ['48.o1.a1', '48.p1.a1', '48.s1.a1', '48.bg1.a1', '48.bh1.a1', '72.u1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3121, -1, 3505, -1, 2397, -1, 3014, -1], 'generators': [25, 384, 2, 576, 48], 'label': '1152.155799.24.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '24.ba1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60968129
    {'ambient': '1152.155799', 'aut_centralizer_order': 24, 'aut_label': '24.bb1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.51', 'aut_weyl_index': 144, 'centralizer': '96.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.w1.a1', '12.bv1.a1'], 'contains': ['48.o1.a1', '48.r1.a1', '48.u1.a1', '72.v1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3051, -1, 3619, -1, 2018, -1, 2659, -1], 'generators': [2, 576, 120, 384, 624], 'label': '1152.155799.24.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '24.bb1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 60968130
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.bc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.x1.a1', '12.bu1.a1'], 'contains': ['48.o1.a1', '48.t1.a1', '48.y1.a1', '72.w1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2995, -1, 3671, -1, 1809, -1, 2521, -1], 'generators': [121, 384, 2, 48, 576], 'label': '1152.155799.24.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '24.bc1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60968131
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '24.bd1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '96.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '12.x1.a1', '12.be1.a1', '12.bf1.a1', '12.bg1.a1', '12.bh1.a1', '12.bv1.a1'], 'contains': ['48.o1.a1', '48.q1.a1', '48.bi1.a1', '48.bj1.a1', '72.x1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7879, -1, 7413, -1, 5316, -1, 6251, -1], 'generators': [2, 48, 24, 576, 384], 'label': '1152.155799.24.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bd1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60968132
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.be1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.w1.a1', '12.bx1.a1'], 'contains': ['48.p1.a1', '48.r1.a1', '48.y1.a1', '72.y1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2666, -1, 3566, -1, 1957, -1, 2482, -1], 'generators': [3, 384, 120, 624, 576], 'label': '1152.155799.24.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '24.be1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.be1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60968133
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.bf1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.y1.a1', '12.bu1.a1'], 'contains': ['48.p1.a1', '48.t1.a1', '48.u1.a1', '72.z1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2704, -1, 3456, -1, 1900, -1, 2395, -1], 'generators': [121, 384, 98, 48, 576], 'label': '1152.155799.24.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '24.bf1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60968134
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '24.bg1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '12.y1.a1', '12.bi1.a1', '12.bj1.a1', '12.bk1.a1', '12.bl1.a1', '12.bx1.a1'], 'contains': ['48.p1.a1', '48.q1.a1', '48.bm1.a1', '48.bn1.a1', '72.ba1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7165, -1, 8181, -1, 5178, -1, 5913, -1], 'generators': [3, 384, 24, 576, 48], 'label': '1152.155799.24.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bg1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968135
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '24.bh1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '96.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '12.y1.a1', '12.bm1.a1', '12.bn1.a1', '12.bo1.a1', '12.bp1.a1', '12.bv1.a1'], 'contains': ['48.q1.a1', '48.u1.a1', '72.bb1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6423, -1, 6618, -1, 4719, -1, 5745, -1], 'generators': [98, 576, 24, 384, 48], 'label': '1152.155799.24.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bh1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60968136
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 8, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.a1.a1', '8.i1.a1', '8.j1.a1', '12.i1.a1', '12.t1.a1', '16.e1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1653, -1, 2138, -1, 3117, -1, 3139, -1], 'generators': [1, 96, 384, 6, 576, 48, 32], 'label': '1152.155799.4.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.i1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 60968137
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '24.bi1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '96.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '12.z1.a1', '12.be1.a1', '12.bi1.a1', '12.bm1.a1', '12.bq1.a1', '12.ca1.a1'], 'contains': ['48.q1.a1', '48.v1.a1', '48.bq1.a1', '48.bu1.a1', '72.bc1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9161, -1, 7777, -1, 6116, -1, 7724, -1], 'generators': [6, 48, 24, 96, 384], 'label': '1152.155799.24.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bi1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60968138
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '24.bj1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '96.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '12.ba1.a1', '12.bf1.a1', '12.bj1.a1', '12.bn1.a1', '12.br1.a1', '12.ca1.a1'], 'contains': ['48.q1.a1', '48.w1.a1', '72.bd1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6823, -1, 6992, -1, 5525, -1, 6544, -1], 'generators': [582, 96, 24, 384, 144], 'label': '1152.155799.24.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bj1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60968139
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '24.bk1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '12.z1.a1', '12.bg1.a1', '12.bk1.a1', '12.bo1.a1', '12.bs1.a1', '12.cb1.a1'], 'contains': ['48.q1.a1', '48.x1.a1', '72.be1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6540, -1, 6565, -1, 4656, -1, 6484, -1], 'generators': [583, 384, 24, 144, 96], 'label': '1152.155799.24.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bk1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968140
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '24.bl1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '12.x1.a1', '12.bq1.a1', '12.br1.a1', '12.bs1.a1', '12.bt1.a1', '12.bx1.a1'], 'contains': ['48.q1.a1', '48.y1.a1', '72.bf1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7222, -1, 6911, -1, 4604, -1, 5853, -1], 'generators': [99, 384, 24, 48, 576], 'label': '1152.155799.24.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bl1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968141
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '24.bm1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '12.ba1.a1', '12.bh1.a1', '12.bl1.a1', '12.bp1.a1', '12.bt1.a1', '12.cb1.a1'], 'contains': ['48.q1.a1', '48.z1.a1', '48.br1.a1', '48.bv1.a1', '72.bg1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7499, -1, 8611, -1, 5711, -1, 7542, -1], 'generators': [7, 384, 24, 96, 48], 'label': '1152.155799.24.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bm1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968142
    {'ambient': '1152.155799', 'aut_centralizer_order': 192, 'aut_label': '24.bn1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.p1.a1', '12.bb1.a1', '12.be1.a1', '12.bl1.a1', '12.bn1.a1', '12.bs1.a1'], 'contains': ['48.d1.a1', '48.q1.a1', '48.bs1.a1', '72.bh1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7070, -1, 7722, -1, 7544, -1, 8184, -1], 'generators': [12, 48, 96, 384, 24], 'label': '1152.155799.24.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bn1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968143
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '24.bo1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.q1.a1', '12.bc1.a1', '12.bf1.a1', '12.bk1.a1', '12.bm1.a1', '12.bt1.a1'], 'contains': ['48.q1.a1', '48.bs1.a1', '72.bi1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8551, -1, 8840, -1, 6613, -1, 7854, -1], 'generators': [588, 48, 96, 384, 24], 'label': '1152.155799.24.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bo1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968144
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '24.bp1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.p1.a1', '12.bc1.a1', '12.bh1.a1', '12.bi1.a1', '12.bo1.a1', '12.br1.a1'], 'contains': ['48.e1.a1', '48.q1.a1', '48.bt1.a1', '72.bj1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8486, -1, 8779, -1, 7471, -1, 9016, -1], 'generators': [13, 384, 96, 24, 48], 'label': '1152.155799.24.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bp1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968145
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '24.bq1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.q1.a1', '12.bb1.a1', '12.bg1.a1', '12.bj1.a1', '12.bp1.a1', '12.bq1.a1'], 'contains': ['48.q1.a1', '48.bt1.a1', '72.bk1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7818, -1, 8243, -1, 6686, -1, 7924, -1], 'generators': [589, 384, 96, 24, 48], 'label': '1152.155799.24.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bq1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968146
    {'ambient': '1152.155799', 'aut_centralizer_order': 24, 'aut_label': '24.br1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.51', 'aut_weyl_index': 144, 'centralizer': '96.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.a1', '12.bd1.a1', '12.ca1.a1'], 'contains': ['48.r1.a1', '48.v1.a1', '48.w1.a1', '72.bl1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4946, -1, 4777, -1, 3310, -1, 5438, -1], 'generators': [6, 96, 600, 384, 48], 'label': '1152.155799.24.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '24.br1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.br1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 60968147
    {'ambient': '1152.155799', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2304.oh', 'aut_weyl_index': 2, 'centralizer': '576.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.h1.a1', '4.k1.a1', '6.c1.a1', '6.j1.a1', '8.d1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3065, 1382, 3609, 4657, 4269, 1057, 3060, 6946], 'generators': [1, 32, 384, 2, 48, 576, 672, 24], 'label': '1152.155799.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '576.8312'}
  • id: 60968148
    {'ambient': '1152.155799', 'aut_centralizer_order': 1, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1152.153175', 'aut_weyl_index': 4, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.d1.a1', '8.e1.a1', '8.f1.a1', '8.k1.a1', '8.l1.a1', '8.m1.a1', '8.n1.a1', '12.j1.a1', '12.u1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3999, -1, 5466, -1, 8922, -1, 3836, -1], 'generators': [1, 32, 48, 2, 384, 12, 24], 'label': '1152.155799.4.j1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '4.j1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1.a1', 'subgroup_fusion': None, 'weyl_group': '144.144'}
  • id: 60968149
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.bs1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.a1', '12.bd1.a1', '12.cb1.a1'], 'contains': ['48.r1.a1', '48.x1.a1', '48.z1.a1', '72.bm1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4828, -1, 4640, -1, 3253, -1, 5383, -1], 'generators': [7, 384, 600, 48, 96], 'label': '1152.155799.24.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '24.bs1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60968150
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '24.bt1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '12.w1.a1', '12.bu1.a1'], 'contains': ['48.s1.a1', '48.u1.a1', '48.y1.a1', '72.bn1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2385, -1, 3365, -1, 1769, -1, 2168, -1], 'generators': [25, 384, 98, 48, 576], 'label': '1152.155799.24.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '24.bt1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60968151
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '24.bu1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '12.bd1.a1', '12.cc1.a1'], 'contains': ['48.s1.a1', '48.v1.a1', '48.z1.a1', '48.bw1.a1', '48.bx1.a1', '72.bo1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5027, -1, 4702, -1, 3845, -1, 6187, -1], 'generators': [25, 384, 6, 96, 48], 'label': '1152.155799.24.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '24.bu1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60968152
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '24.bv1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '12.bd1.a1', '12.cc1.a1'], 'contains': ['48.s1.a1', '48.w1.a1', '48.x1.a1', '72.bp1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4323, -1, 4421, -1, 3119, -1, 5061, -1], 'generators': [25, 384, 582, 48, 96], 'label': '1152.155799.24.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '24.bv1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60968153
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.bw1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.a1', '12.z1.a1', '12.cc1.a1'], 'contains': ['48.t1.a1', '48.v1.a1', '48.x1.a1', '72.bq1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4895, -1, 4826, -1, 3212, -1, 5293, -1], 'generators': [601, 384, 6, 48, 96], 'label': '1152.155799.24.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '24.bw1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60968154
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.bx1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.a1', '12.ba1.a1', '12.cc1.a1'], 'contains': ['48.t1.a1', '48.w1.a1', '48.z1.a1', '72.br1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4786, -1, 4601, -1, 3165, -1, 5338, -1], 'generators': [601, 384, 582, 48, 96], 'label': '1152.155799.24.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '24.bx1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60968155
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '24.by1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '96.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.s1.a1', '12.bu1.a1', '12.bv1.a1'], 'contains': ['48.b1.a1', '48.o1.a1', '48.u1.a1', '48.cl1.a1', '48.cp1.a1', '72.bs1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1329, -1, 1874, -1, 1052, -1, 1761, -1], 'generators': [2, 576, 48, 96, 384], 'label': '1152.155799.24.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '24.by1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.by1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 60968156
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '24.bz1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.b1.a1', '12.g1.a1', '12.bw1.a1'], 'contains': ['48.c1.a1', '48.cq1.a1', '72.bs1.a1', '96.j1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [542, -1, 856, -1, 1455, -1, 1378, -1], 'generators': [2, 576, 48, 32, 672], 'label': '1152.155799.24.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.bz1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 60968157
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '24.ca1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.s1.a1', '12.bu1.a1', '12.bx1.a1'], 'contains': ['48.b1.a1', '48.p1.a1', '48.y1.a1', '48.cm1.a1', '48.cr1.a1', '72.bt1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1438, -1, 2108, -1, 926, -1, 1696, -1], 'generators': [3, 384, 48, 96, 576], 'label': '1152.155799.24.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '24.ca1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60968158
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '24.cb1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.g1.a1', '12.bw1.a1', '12.by1.a1'], 'contains': ['48.c1.a1', '48.cs1.a1', '72.bt1.a1', '96.l1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [488, -1, 805, -1, 1396, -1, 1435, -1], 'generators': [3, 576, 48, 32, 672], 'label': '1152.155799.24.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.cb1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 60968159
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 8, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.c1.a1', '8.g1.a1', '8.h1.a1', '12.bu1.a1', '12.bw1.a1', '16.f1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1179, -1, 1809, -1, 2011, -1, 2200, -1], 'generators': [25, 672, 384, 2, 576, 48, 32], 'label': '1152.155799.4.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': '4.k1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 60968160
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.cc1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.bz1.a1'], 'contains': ['48.ba1.a1', '48.ct1.a1', '72.bt1.a1', '96.m1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1992, -1, 2285, -1, 859, -1, 1565, -1], 'generators': [3, 576, 48, 416, 672], 'label': '1152.155799.24.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bz1.a1', 'old_label': '24.cc1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 60968161
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '24.cd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '96.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '12.t1.a1', '12.ca1.a1', '12.cc1.a1'], 'contains': ['48.b1.a1', '48.v1.a1', '48.w1.a1', '72.bv1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2774, -1, 3206, -1, 2976, -1, 4797, -1], 'generators': [6, 96, 576, 384, 48], 'label': '1152.155799.24.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '24.cd1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 60968162
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '24.ce1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.t1.a1', '12.cb1.a1', '12.cc1.a1'], 'contains': ['48.b1.a1', '48.x1.a1', '48.z1.a1', '72.bw1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2830, -1, 3154, -1, 2638, -1, 4407, -1], 'generators': [7, 384, 576, 48, 96], 'label': '1152.155799.24.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '24.ce1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60968163
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '24.cf1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '72.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.h1.a1', '12.bw1.a1', '12.cf1.a1'], 'contains': ['48.c1.a1', '72.bu1.a1', '96.s1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1174, -1, 1981, -1, 2481, -1, 2282, -1], 'generators': [25, 576, 32, 48, 96], 'label': '1152.155799.24.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.cf1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60968164
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '24.cg1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '12.e1.a1', '12.i1.a1', '12.cf1.a1'], 'contains': ['48.c1.a1', '72.bv1.a1', '96.t1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1519, -1, 1784, -1, 3506, -1, 2888, -1], 'generators': [6, 576, 48, 32, 96], 'label': '1152.155799.24.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.cg1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 60968165
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '24.ch1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.i1.a1', '12.cd1.a1', '12.cf1.a1'], 'contains': ['48.c1.a1', '72.bw1.a1', '96.u1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1609, -1, 1817, -1, 3367, -1, 2927, -1], 'generators': [7, 576, 48, 32, 96], 'label': '1152.155799.24.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.ch1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 60968166
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '24.ci1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.bz1.a1', '12.cg1.a1', '12.ch1.a1'], 'contains': ['48.ba1.a1', '72.a1.a1', '96.v1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4510, -1, 5256, -1, 4085, -1, 3869, -1], 'generators': [24, 576, 416, 48, 96], 'label': '1152.155799.24.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '24.ci1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60968167
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.cj1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.cg1.a1'], 'contains': ['48.ba1.a1', '72.bw1.a1', '96.w1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2881, -1, 2684, -1, 2547, -1, 3498, -1], 'generators': [7, 576, 48, 416, 96], 'label': '1152.155799.24.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cg1.a1', 'old_label': '24.cj1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 60968168
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.ck1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '12.ci1.a1', '12.cj1.a1'], 'contains': ['48.bb1.a1', '48.bc1.a1', '48.bh1.a1', '48.bi1.a1', '48.bm1.a1', '72.bx1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9230, -1, 9242, -1, 6176, -1, 7258, -1], 'generators': [577, 384, 2, 24, 48], 'label': '1152.155799.24.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.ck1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60968169
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.cl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1'], 'contains': ['48.bb1.a1', '48.bd1.a1', '48.bg1.a1', '48.bj1.a1', '48.bn1.a1', '72.by1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7560, -1, 8005, -1, 4226, -1, 3942, -1], 'generators': [577, 384, 2, 600, 48], 'label': '1152.155799.24.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '24.cl1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60968170
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '4.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 8, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.c1.a1', '8.i1.a1', '8.j1.a1', '12.cc1.a1', '12.cf1.a1', '16.m1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1831, -1, 2331, -1, 3193, -1, 3202, -1], 'generators': [25, 96, 384, 6, 576, 48, 32], 'label': '1152.155799.4.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.l1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 60968171
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.cm1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '12.ci1.a1', '12.cj1.a1'], 'contains': ['48.bc1.a1', '48.bf1.a1', '48.bq1.a1', '48.br1.a1', '48.bx1.a1', '72.bz1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9633, -1, 9342, -1, 6753, -1, 8341, -1], 'generators': [97, 384, 6, 24, 48], 'label': '1152.155799.24.cm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.cm1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60968172
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '24.cn1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.a1', '12.bb1.a1', '12.ci1.a1'], 'contains': ['48.d1.a1', '48.bc1.a1', '48.bt1.a1', '72.ca1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8818, -1, 9794, -1, 8561, -1, 9515, -1], 'generators': [97, 384, 12, 24, 48], 'label': '1152.155799.24.cn1.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': '24.cn1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cn1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968173
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '24.co1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.a1', '12.bc1.a1', '12.cj1.a1'], 'contains': ['48.e1.a1', '48.bc1.a1', '48.bs1.a1', '72.cb1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9061, -1, 9573, -1, 8717, -1, 9825, -1], 'generators': [97, 384, 108, 24, 48], 'label': '1152.155799.24.co1.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': '24.co1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.co1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968174
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '24.cp1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '12.bb1.a1', '12.bc1.a1'], 'contains': ['48.bc1.a1', '48.bs1.a1', '48.bt1.a1', '72.cc1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8909, -1, 9522, -1, 7405, -1, 9212, -1], 'generators': [577, 384, 108, 24, 48], 'label': '1152.155799.24.cp1.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': '24.cp1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cp1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968175
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.cq1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1'], 'contains': ['48.bd1.a1', '48.bf1.a1', '48.bu1.a1', '48.bv1.a1', '48.bw1.a1', '72.cd1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9867, -1, 9177, -1, 4879, -1, 7315, -1], 'generators': [97, 384, 6, 120, 48], 'label': '1152.155799.24.cq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '24.cq1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cq1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60968176
    {'ambient': '1152.155799', 'aut_centralizer_order': 24, 'aut_label': '24.cr1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '96.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '12.u1.a1', '12.be1.a1', '12.ci1.a1'], 'contains': ['48.d1.a1', '48.bi1.a1', '48.bq1.a1', '72.ce1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8691, -1, 7601, -1, 9194, -1, 8416, -1], 'generators': [2, 48, 12, 384, 24], 'label': '1152.155799.24.cr1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.cr1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cr1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968177
    {'ambient': '1152.155799', 'aut_centralizer_order': 24, 'aut_label': '24.cs1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '96.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.a1', '12.be1.a1', '12.cj1.a1'], 'contains': ['48.bi1.a1', '48.bq1.a1', '48.bs1.a1', '72.cf1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9552, -1, 9423, -1, 8639, -1, 9326, -1], 'generators': [2, 48, 588, 384, 24], 'label': '1152.155799.24.cs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.cs1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cs1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968178
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.ct1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '12.u1.a1', '12.bh1.a1', '12.cj1.a1'], 'contains': ['48.e1.a1', '48.bi1.a1', '48.br1.a1', '72.cg1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8418, -1, 8716, -1, 9066, -1, 8651, -1], 'generators': [13, 384, 2, 24, 48], 'label': '1152.155799.24.ct1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.ct1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ct1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60968179
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.cu1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.a1', '12.bh1.a1', '12.ci1.a1'], 'contains': ['48.bi1.a1', '48.br1.a1', '48.bt1.a1', '72.ch1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9370, -1, 9644, -1, 8315, -1, 9410, -1], 'generators': [589, 384, 2, 24, 48], 'label': '1152.155799.24.cu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.cu1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cu1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60968180
    {'ambient': '1152.155799', 'aut_centralizer_order': 12, 'aut_label': '24.cv1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '8.k1.a1', '12.j1.a1'], 'contains': ['48.bl1.a1', '48.by1.a1', '48.ca1.a1', '72.ce1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3188, -1, 5355, -1, 9912, -1, 3766, -1], 'generators': [2, 32, 12, 24, 48], 'label': '1152.155799.24.cv1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '24.cv1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cv1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
  • id: 60968181
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 16, 'centralizer': '36.a1.a1', 'complements': ['192.j1.a1', '192.l1.a1', '192.m1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.b1.a1'], 'contains': ['12.a1.a1', '12.c1.a1', '12.d1.a1', '12.p1.a1', '12.q1.a1', '12.bb1.a1', '12.bc1.a1', '18.g1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6892, 9249, 8315, 4657, 6803, 9316, 8035, 3420], 'generators': [1, 48, 24, 12, 384, 96, 576], 'label': '1152.155799.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['12.a1.a1', '12.c1.a1', '12.d1.a1', '24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '576.8312', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 60968182
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '24.cw1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.r1.a1', '8.l1.a1', '12.j1.a1'], 'contains': ['48.bl1.a1', '48.bz1.a1', '48.cb1.a1', '72.cg1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3753, -1, 4079, -1, 9832, -1, 3728, -1], 'generators': [13, 32, 2, 24, 48], 'label': '1152.155799.24.cw1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '24.cw1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cw1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
  • id: 60968183
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.cx1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '12.u1.a1', '12.bi1.a1', '12.cj1.a1'], 'contains': ['48.e1.a1', '48.bm1.a1', '48.bq1.a1', '72.ci1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8772, -1, 8959, -1, 9125, -1, 8801, -1], 'generators': [13, 384, 6, 24, 48], 'label': '1152.155799.24.cx1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.cx1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cx1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60968184
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.cy1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.a1', '12.bi1.a1', '12.ci1.a1'], 'contains': ['48.bm1.a1', '48.bq1.a1', '48.bt1.a1', '72.cj1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9438, -1, 9738, -1, 8511, -1, 9466, -1], 'generators': [109, 384, 6, 24, 48], 'label': '1152.155799.24.cy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.cy1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cy1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60968185
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.cz1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '12.u1.a1', '12.bl1.a1', '12.ci1.a1'], 'contains': ['48.d1.a1', '48.bm1.a1', '48.br1.a1', '72.ck1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7004, -1, 9012, -1, 8767, -1, 8130, -1], 'generators': [3, 384, 12, 24, 48], 'label': '1152.155799.24.cz1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.cz1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cz1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60968186
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.da1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.a1', '12.bl1.a1', '12.cj1.a1'], 'contains': ['48.bm1.a1', '48.br1.a1', '48.bs1.a1', '72.cl1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9474, -1, 9481, -1, 8470, -1, 9260, -1], 'generators': [3, 384, 588, 24, 48], 'label': '1152.155799.24.da1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.da1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.da1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60968187
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '24.db1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.u1.a1', '8.m1.a1', '12.j1.a1'], 'contains': ['48.bo1.a1', '48.by1.a1', '48.cb1.a1', '72.ci1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4073, -1, 4162, -1, 9872, -1, 3804, -1], 'generators': [13, 32, 6, 24, 48], 'label': '1152.155799.24.db1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '24.db1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.db1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
  • id: 60968188
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '24.dc1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.v1.a1', '8.n1.a1', '12.j1.a1'], 'contains': ['48.bo1.a1', '48.bz1.a1', '48.ca1.a1', '72.ck1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3254, -1, 4128, -1, 9605, -1, 3689, -1], 'generators': [3, 32, 12, 24, 48], 'label': '1152.155799.24.dc1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '24.dc1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dc1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
  • id: 60968189
    {'ambient': '1152.155799', 'aut_centralizer_order': 2, 'aut_label': '24.dd1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '96.209', 'aut_weyl_index': 48, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.w1.a1', '8.n1.a1'], 'contains': ['48.bp1.a1', '48.cd1.a1', '48.ce1.a1', '72.ck1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [4235, -1, 5683, -1, 6557, -1, 4048, -1], 'generators': [3, 416, 12, 24, 48], 'label': '1152.155799.24.dd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.dd1.a1', 'old_label': '24.dd1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dd1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
  • id: 60968190
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.de1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '12.g1.a1'], 'contains': ['48.cf1.a1', '48.cq1.a1', '48.cs1.a1', '72.cn1.a1', '96.x1.a1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [247, -1, 246, -1, 364, -1, 346, -1], 'generators': [1, 576, 2, 32, 672], 'label': '1152.155799.24.de1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1.a1', 'old_label': '24.de1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.de1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60968191
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.de1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.b1', '12.g1.a1'], 'contains': ['48.cf1.b1', '48.cq1.a1', '48.cs1.a1', '72.cn1.b1', '96.x1.b1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [247, -1, 311, -1, 364, -1, 119, -1], 'generators': [49, 576, 2, 32, 672], 'label': '1152.155799.24.de1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1.a1', 'old_label': '24.de1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.de1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60968192
    {'ambient': '1152.155799', 'aut_centralizer_order': 12, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '384.20051', 'aut_weyl_index': 12, 'centralizer': '96.a1.a1', 'complements': ['192.b1.a1', '192.h1.a1', '192.b1.b1', '192.h1.b1', '192.k1.a1', '192.m1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.e1.a1', '12.f1.a1', '18.l1.a1', '24.cv1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3418, 6337, 5296, 9190, 7552, 6964, 3924, 9581], 'generators': [2, 672, 32, 12, 576, 24, 48], 'label': '1152.155799.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.d1.a1'], 'normal_contains': ['12.b1.a1', '12.e1.a1', '12.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '576.8312', 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '96.187'}
  • id: 60968193
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.df1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1.a1'], 'contains': ['48.cg1.a1', '48.ch1.a1', '48.ci1.a1', '48.cl1.a1', '48.cm1.a1', '48.cn1.b1', '48.co1.b1', '72.cm1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1259, -1, 1556, -1, 651, -1, 1101, -1], 'generators': [1, 384, 2, 144, 576], 'label': '1152.155799.24.df1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '24.df1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.df1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60968194
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.df1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1.a1'], 'contains': ['48.cg1.b1', '48.ch1.b1', '48.ci1.b1', '48.cl1.a1', '48.cm1.a1', '48.cn1.a1', '48.co1.a1', '72.cm1.b1'], 'core': '192.b1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [1259, -1, 1616, -1, 651, -1, 1043, -1], 'generators': [97, 384, 2, 144, 576], 'label': '1152.155799.24.df1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '24.df1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.df1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60968195
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.dg1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '12.s1.a1'], 'contains': ['48.f1.a1', '48.ch1.a1', '48.ci1.a1', '48.cn1.a1', '48.co1.a1', '48.cp1.a1', '48.cr1.a1', '72.cn1.a1'], 'core': '48.f1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [626, -1, 1007, -1, 424, -1, 827, -1], 'generators': [1, 384, 2, 96, 576], 'label': '1152.155799.24.dg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '24.dg1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dg1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60968196
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '24.dg1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.b1', '12.s1.a1'], 'contains': ['48.f1.b1', '48.ch1.b1', '48.ci1.b1', '48.cn1.b1', '48.co1.b1', '48.cp1.a1', '48.cr1.a1', '72.cn1.b1'], 'core': '48.f1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [626, -1, 1086, -1, 424, -1, 686, -1], 'generators': [49, 384, 2, 96, 576], 'label': '1152.155799.24.dg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '24.dg1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dg1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60968197
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '32.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 96, 'centralizer': '48.d1.a1', 'complements': ['36.m1.a1', '36.bt1.a1', '36.n1.a1', '36.bu1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.b1.b1', '16.n1.a1', '16.o1.a1'], 'contains': ['96.d1.a1', '96.e1.a1', '96.bh1.a1', '128.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [111, 669, 122, 1033, 89, 1218, 175, 2423], 'generators': [32, 384, 672, 576], 'label': '1152.155799.32.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1', '16.b1.b1', '16.b1.a1'], 'normal_contains': ['96.d1.a1', '96.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '1152.155799', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 60968198
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '48.ca1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '16.c1.a1', '16.d1.a1', '16.e1.a1'], 'contains': ['64.a1.a1', '64.b1.a1', '64.b1.b1', '96.a1.a1', '96.f1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [896, -1, 1371, -1, 2670, -1, 1610, -1], 'generators': [1, 48, 32, 384], 'label': '1152.155799.32.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '32.b1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968199
    {'ambient': '1152.155799', 'aut_centralizer_order': 24, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '16.c1.a1', '16.f1.a1', '16.g1.a1'], 'contains': ['64.a1.a1', '64.c1.a1', '96.i1.a1', '96.j1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [715, -1, 1119, -1, 2537, -1, 1699, -1], 'generators': [2, 48, 384, 32], 'label': '1152.155799.32.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.d1.a1', 'old_label': '32.c1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60968200
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '72.46', 'aut_weyl_index': 64, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '16.c1.a1', '16.f1.a1', '16.h1.a1'], 'contains': ['64.a1.a1', '64.d1.a1', '96.k1.a1', '96.l1.a1', '96.m1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [775, -1, 1301, -1, 2402, -1, 1820, -1], 'generators': [3, 48, 32, 384], 'label': '1152.155799.32.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.d1.a1', 'old_label': '32.d1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 60968201
    {'ambient': '1152.155799', 'aut_centralizer_order': 144, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '16.d1.a1', '16.g1.a1', '16.h1.a1', '16.i1.a1', '16.j1.a1', '16.k1.a1', '16.l1.a1'], 'contains': ['64.a1.a1', '96.b1.a1', '96.r1.a1', '96.v1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3565, -1, 5314, -1, 6462, -1, 3971, -1], 'generators': [24, 32, 384, 48], 'label': '1152.155799.32.e1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '32.e1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968202
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '48.ca1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '16.d1.a1', '16.f1.a1', '16.m1.a1'], 'contains': ['64.a1.a1', '96.c1.a1', '96.s1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1363, -1, 1936, -1, 3286, -1, 3043, -1], 'generators': [25, 32, 48, 384], 'label': '1152.155799.32.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '32.f1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968203
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20051', 'aut_weyl_index': 12, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.g1.a1', '12.h1.a1', '12.bw1.a1', '12.by1.a1', '18.e1.a1', '24.g1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3051, -1, 3324, -1, 4511, -1, 2981, -1], 'generators': [1, 672, 32, 2, 576, 24, 48], 'label': '1152.155799.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '96.187'}
  • id: 60968204
    {'ambient': '1152.155799', 'aut_centralizer_order': 24, 'aut_label': '32.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '16.e1.a1', '16.i1.a1', '16.m1.a1'], 'contains': ['64.a1.a1', '96.p1.a1', '96.t1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1702, -1, 2223, -1, 4477, -1, 3759, -1], 'generators': [6, 384, 48, 32], 'label': '1152.155799.32.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1.a1', 'old_label': '32.g1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.g1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60968205
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '32.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '72.46', 'aut_weyl_index': 64, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '16.e1.a1', '16.j1.a1', '16.m1.a1'], 'contains': ['64.a1.a1', '96.q1.a1', '96.u1.a1', '96.w1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1555, -1, 2331, -1, 4399, -1, 3896, -1], 'generators': [7, 48, 32, 384], 'label': '1152.155799.32.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1.a1', 'old_label': '32.h1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.h1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 60968206
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '36.10', 'aut_weyl_index': 128, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '16.c1.a1'], 'contains': ['64.b1.a1', '64.c1.a1', '64.d1.a1', '96.x1.a1', '96.ba1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [309, -1, 346, -1, 964, -1, 319, -1], 'generators': [1, 2, 32, 384], 'label': '1152.155799.32.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1.a1', 'old_label': '32.i1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 60968207
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '36.10', 'aut_weyl_index': 128, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.b1', '16.c1.a1'], 'contains': ['64.b1.b1', '64.c1.a1', '64.d1.a1', '96.x1.b1', '96.ba1.b1'], 'core': '192.b1.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [309, -1, 441, -1, 964, -1, 252, -1], 'generators': [49, 2, 32, 384], 'label': '1152.155799.32.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1.a1', 'old_label': '32.i1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 60968208
    {'ambient': '1152.155799', 'aut_centralizer_order': 192, 'aut_label': '36.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '6.a1.a1', 'complements': ['32.i1.a1', '32.i1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.f1.a1', '12.ch1.a1', '18.g1.a1', '18.l1.a1', '18.o1.a1'], 'contains': ['72.a1.a1', '72.bh1.a1', '72.bi1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5650, 7536, 6104, 8126, 7614, 7445, 6884, 7561], 'generators': [12, 96, 576], 'label': '1152.155799.36.a1.a1', 'mobius_quo': 0, 'mobius_sub': 18, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['12.c1.a1', '12.f1.a1'], 'normal_contains': ['72.a1.a1', '144.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '576.8312', 'quotient_action_image': '6.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968209
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.51', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '18.e1.a1'], 'contains': ['72.b1.a1', '72.d1.a1', '72.e1.a1', '72.v1.a1', '72.w1.a1', '72.y1.a1', '72.z1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3011, -1, 3445, -1, 2151, -1, 2580, -1], 'generators': [1, 2, 120], 'label': '1152.155799.36.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '36.b1.a1', 'projective_image': '576.8312', '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': '8.5'}
  • id: 60968210
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '18.a1.a1', '18.b1.a1', '18.e1.a1'], 'contains': ['72.b1.a1', '72.c1.a1', '72.i1.a1', '72.j1.a1', '72.u1.a1', '72.x1.a1', '72.ba1.a1', '72.bx1.a1', '72.by1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7277, -1, 7526, -1, 5381, -1, 5981, -1], 'generators': [1, 2, 24, 576], 'label': '1152.155799.36.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.c1.a1', 'projective_image': '576.8312', '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': '16.11'}
  • id: 60968211
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '18.c1.a1', '18.d1.a1', '18.e1.a1'], 'contains': ['72.c1.a1', '72.e1.a1', '72.bb1.a1', '72.bf1.a1', '72.bn1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5715, -1, 6192, -1, 4946, -1, 5626, -1], 'generators': [1, 98, 24], 'label': '1152.155799.36.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.d1.a1', 'projective_image': '576.8312', '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': '16.11'}
  • id: 60968212
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '18.a1.a1', '18.c1.a1', '18.f1.a1'], 'contains': ['72.c1.a1', '72.f1.a1', '72.k1.a1', '72.n1.a1', '72.bc1.a1', '72.bg1.a1', '72.bo1.a1', '72.bz1.a1', '72.cd1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8582, -1, 8652, -1, 6391, -1, 7786, -1], 'generators': [1, 6, 24, 96], 'label': '1152.155799.36.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.e1.a1', 'projective_image': '576.8312', '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': '16.11'}
  • id: 60968213
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '18.b1.a1', '18.d1.a1', '18.f1.a1'], 'contains': ['72.c1.a1', '72.g1.a1', '72.bd1.a1', '72.be1.a1', '72.bp1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5997, -1, 6254, -1, 5983, -1, 6614, -1], 'generators': [1, 582, 24], 'label': '1152.155799.36.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.f1.a1', 'projective_image': '576.8312', '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': '16.11'}
  • id: 60968214
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20051', 'aut_weyl_index': 12, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.e1.a1', '12.h1.a1', '12.i1.a1', '12.cd1.a1', '12.cf1.a1', '18.f1.a1', '24.h1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3150, -1, 3484, -1, 5282, -1, 3286, -1], 'generators': [1, 96, 32, 6, 576, 24, 48], 'label': '1152.155799.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '96.187'}
  • id: 60968215
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.a1', '18.a1.a1', '18.d1.a1', '18.g1.a1'], 'contains': ['72.c1.a1', '72.l1.a1', '72.m1.a1', '72.bh1.a1', '72.bj1.a1', '72.ca1.a1', '72.cb1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6868, -1, 7130, -1, 8992, -1, 9670, -1], 'generators': [1, 12, 96], 'label': '1152.155799.36.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.g1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968216
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '18.b1.a1', '18.c1.a1', '18.g1.a1'], 'contains': ['72.c1.a1', '72.m1.a1', '72.bi1.a1', '72.bk1.a1', '72.cc1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7607, -1, 7358, -1, 7683, -1, 9150, -1], 'generators': [1, 588, 96], 'label': '1152.155799.36.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.h1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968217
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.51', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.a1', '18.f1.a1'], 'contains': ['72.d1.a1', '72.f1.a1', '72.g1.a1', '72.bl1.a1', '72.bm1.a1', '72.bq1.a1', '72.br1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4972, -1, 4965, -1, 3662, -1, 5508, -1], 'generators': [1, 6, 600], 'label': '1152.155799.36.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '36.i1.a1', 'projective_image': '576.8312', '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': '8.5'}
  • id: 60968218
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.s1.a1', '18.e1.a1'], 'contains': ['72.b1.a1', '72.e1.a1', '72.h1.a1', '72.o1.a1', '72.p1.a1', '72.bs1.a1', '72.bt1.a1', '72.cm1.a1', '72.cm1.b1', '72.cn1.a1', '72.cn1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1508, -1, 1978, -1, 1331, -1, 1627, -1], 'generators': [1, 2, 48, 96], 'label': '1152.155799.36.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '36.j1.a1', 'projective_image': '576.8312', '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': '8.5'}
  • id: 60968219
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.h1.a1', '18.e1.a1', '18.f1.a1', '18.g1.a1'], 'contains': ['72.a1.a1', '72.c1.a1', '72.d1.a1', '72.h1.a1', '72.q1.a1', '72.r1.a1', '72.bu1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3835, -1, 4102, -1, 4291, -1, 5114, -1], 'generators': [1, 24, 96, 576], 'label': '1152.155799.36.k1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.k1.a1', 'projective_image': '576.8312', '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': '6.1'}
  • id: 60968220
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.t1.a1', '18.f1.a1'], 'contains': ['72.f1.a1', '72.g1.a1', '72.h1.a1', '72.s1.a1', '72.t1.a1', '72.bv1.a1', '72.bw1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2347, -1, 2784, -1, 3428, -1, 4876, -1], 'generators': [1, 6, 576], 'label': '1152.155799.36.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '36.l1.a1', 'projective_image': '576.8312', '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': '8.5'}
  • id: 60968221
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.u1.a1', '18.a1.a1'], 'contains': ['72.i1.a1', '72.k1.a1', '72.l1.a1', '72.ce1.a1', '72.cg1.a1', '72.ci1.a1', '72.ck1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6792, -1, 7442, -1, 9674, -1, 8510, -1], 'generators': [1, 2, 12], 'label': '1152.155799.36.m1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.m1.a1', 'projective_image': '576.8312', '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': '8.3'}
  • id: 60968222
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.a1', '18.a1.a1'], 'contains': ['72.i1.a1', '72.k1.a1', '72.m1.a1', '72.cf1.a1', '72.ch1.a1', '72.cj1.a1', '72.cl1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9531, -1, 9439, -1, 8909, -1, 9957, -1], 'generators': [1, 2, 588], 'label': '1152.155799.36.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.n1.a1', 'projective_image': '576.8312', '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': '8.3'}
  • id: 60968223
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.51', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.w1.a1', '18.e1.a1'], 'contains': ['72.o1.a1', '72.p1.a1', '72.r1.a1', '72.u1.a1', '72.v1.a1', '72.y1.a1', '72.bn1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2649, -1, 3361, -1, 2085, -1, 2438, -1], 'generators': [97, 2, 120], 'label': '1152.155799.36.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '36.o1.a1', 'projective_image': '576.8312', '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': '8.5'}
  • id: 60968224
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1.a1', '18.e1.a1', '18.h1.a1', '18.i1.a1'], 'contains': ['72.o1.a1', '72.q1.a1', '72.w1.a1', '72.x1.a1', '72.bf1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6529, -1, 6575, -1, 5117, -1, 5804, -1], 'generators': [97, 2, 24], 'label': '1152.155799.36.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.p1.a1', 'projective_image': '576.8312', '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': '16.11'}
  • id: 60968225
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1537', 'aut_weyl_index': 24, 'centralizer': '72.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.f1.a1', '12.h1.a1', '12.ce1.a1', '18.g1.a1', '24.i1.a1'], 'core': '12.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4696, -1, 5712, -1, 9038, -1, 4250, -1], 'generators': [1, 96, 48, 12, 576, 32, 24], 'label': '1152.155799.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60968226
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.y1.a1', '18.e1.a1', '18.j1.a1', '18.k1.a1'], 'contains': ['72.p1.a1', '72.q1.a1', '72.z1.a1', '72.ba1.a1', '72.bb1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6068, -1, 6923, -1, 6044, -1, 5686, -1], 'generators': [97, 98, 24], 'label': '1152.155799.36.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.q1.a1', 'projective_image': '576.8312', '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': '16.11'}
  • id: 60968227
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.z1.a1', '18.f1.a1', '18.h1.a1', '18.j1.a1'], 'contains': ['72.q1.a1', '72.s1.a1', '72.bc1.a1', '72.be1.a1', '72.bq1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7209, -1, 6618, -1, 6281, -1, 6722, -1], 'generators': [577, 6, 24], 'label': '1152.155799.36.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.r1.a1', 'projective_image': '576.8312', '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': '16.11'}
  • id: 60968228
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ba1.a1', '18.f1.a1', '18.i1.a1', '18.k1.a1'], 'contains': ['72.q1.a1', '72.t1.a1', '72.bd1.a1', '72.bg1.a1', '72.br1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6381, -1, 6965, -1, 6232, -1, 6769, -1], 'generators': [577, 582, 24], 'label': '1152.155799.36.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.s1.a1', 'projective_image': '576.8312', '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': '16.11'}
  • id: 60968229
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bb1.a1', '18.g1.a1', '18.h1.a1', '18.k1.a1'], 'contains': ['72.q1.a1', '72.bh1.a1', '72.bk1.a1', '72.ca1.a1', '72.cc1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6717, -1, 7072, -1, 7950, -1, 8947, -1], 'generators': [577, 12, 96], 'label': '1152.155799.36.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.t1.a1', 'projective_image': '576.8312', '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': '2.1'}
  • id: 60968230
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bc1.a1', '18.g1.a1', '18.i1.a1', '18.j1.a1'], 'contains': ['72.q1.a1', '72.bi1.a1', '72.bj1.a1', '72.cb1.a1', '72.cc1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6976, -1, 7285, -1, 7812, -1, 9084, -1], 'generators': [577, 588, 96], 'label': '1152.155799.36.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.u1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.u1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968231
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '36.v1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.51', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bd1.a1', '18.f1.a1'], 'contains': ['72.r1.a1', '72.s1.a1', '72.t1.a1', '72.bl1.a1', '72.bm1.a1', '72.bo1.a1', '72.bp1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4675, -1, 4758, -1, 3601, -1, 5567, -1], 'generators': [577, 6, 600], 'label': '1152.155799.36.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '36.v1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.v1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60968232
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '36.w1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.be1.a1', '18.a1.a1', '18.h1.a1', '18.l1.a1'], 'contains': ['72.x1.a1', '72.bc1.a1', '72.bh1.a1', '72.ce1.a1', '72.cf1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8191, -1, 7200, -1, 8402, -1, 8265, -1], 'generators': [2, 12, 576], 'label': '1152.155799.36.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.w1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.w1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968233
    {'ambient': '1152.155799', 'aut_centralizer_order': 24, 'aut_label': '36.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bf1.a1', '18.b1.a1', '18.i1.a1', '18.l1.a1'], 'contains': ['72.x1.a1', '72.bd1.a1', '72.bi1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6458, -1, 6670, -1, 7112, -1, 7209, -1], 'generators': [2, 108], 'label': '1152.155799.36.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.x1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.x1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968234
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bg1.a1', '18.b1.a1', '18.h1.a1', '18.m1.a1'], 'contains': ['72.x1.a1', '72.be1.a1', '72.bk1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7055, -1, 6461, -1, 7031, -1, 7054, -1], 'generators': [109, 2], 'label': '1152.155799.36.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.y1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.y1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968235
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '36.z1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bh1.a1', '18.a1.a1', '18.i1.a1', '18.m1.a1'], 'contains': ['72.x1.a1', '72.bg1.a1', '72.bj1.a1', '72.cg1.a1', '72.ch1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8043, -1, 8526, -1, 8130, -1, 8735, -1], 'generators': [13, 2, 576], 'label': '1152.155799.36.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.z1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.z1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968236
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.l1.a1', '12.n1.a1', '12.p1.a1', '12.u1.a1', '12.v1.a1', '12.be1.a1', '12.bh1.a1', '12.bi1.a1', '12.bl1.a1', '12.ci1.a1', '12.cj1.a1', '18.a1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8540, -1, 8509, -1, 6918, -1, 8339, -1], 'generators': [1, 48, 24, 2, 384, 12, 576], 'label': '1152.155799.6.f1.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': '6.f1.a1', 'projective_image': '576.8312', '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': '96.209'}
  • id: 60968237
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '36.ba1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bi1.a1', '18.a1.a1', '18.j1.a1', '18.n1.a1'], 'contains': ['72.ba1.a1', '72.bc1.a1', '72.bj1.a1', '72.ci1.a1', '72.cj1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8325, -1, 8207, -1, 8228, -1, 8867, -1], 'generators': [13, 6, 96], 'label': '1152.155799.36.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.ba1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968238
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '36.bb1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bj1.a1', '18.b1.a1', '18.k1.a1', '18.n1.a1'], 'contains': ['72.ba1.a1', '72.bd1.a1', '72.bk1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6280, -1, 6787, -1, 7314, -1, 7132, -1], 'generators': [589, 582], 'label': '1152.155799.36.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bb1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968239
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '36.bc1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bk1.a1', '18.b1.a1', '18.j1.a1', '18.o1.a1'], 'contains': ['72.ba1.a1', '72.be1.a1', '72.bi1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7107, -1, 6752, -1, 6910, -1, 6976, -1], 'generators': [3, 108], 'label': '1152.155799.36.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bc1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968240
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '36.bd1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bl1.a1', '18.a1.a1', '18.k1.a1', '18.o1.a1'], 'contains': ['72.ba1.a1', '72.bg1.a1', '72.bh1.a1', '72.ck1.a1', '72.cl1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6612, -1, 8444, -1, 8033, -1, 8064, -1], 'generators': [3, 12, 576], 'label': '1152.155799.36.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bd1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968241
    {'ambient': '1152.155799', 'aut_centralizer_order': 24, 'aut_label': '36.be1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bm1.a1', '18.c1.a1', '18.j1.a1', '18.l1.a1'], 'contains': ['72.bb1.a1', '72.bc1.a1', '72.bi1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7905, -1, 7847, -1, 7234, -1, 7597, -1], 'generators': [98, 108], 'label': '1152.155799.36.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.be1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.be1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968242
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '36.bf1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bn1.a1', '18.d1.a1', '18.k1.a1', '18.l1.a1'], 'contains': ['72.bb1.a1', '72.bd1.a1', '72.bh1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5795, -1, 6427, -1, 7355, -1, 7093, -1], 'generators': [98, 12], 'label': '1152.155799.36.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.bf1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968243
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '36.bg1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bo1.a1', '18.d1.a1', '18.j1.a1', '18.m1.a1'], 'contains': ['72.bb1.a1', '72.be1.a1', '72.bj1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6154, -1, 6302, -1, 7072, -1, 7015, -1], 'generators': [13, 98], 'label': '1152.155799.36.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bg1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968244
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '36.bh1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bp1.a1', '18.c1.a1', '18.k1.a1', '18.m1.a1'], 'contains': ['72.bb1.a1', '72.bg1.a1', '72.bk1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6422, -1, 7881, -1, 7193, -1, 7487, -1], 'generators': [109, 98], 'label': '1152.155799.36.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bh1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968245
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '36.bi1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bq1.a1', '18.c1.a1', '18.h1.a1', '18.n1.a1'], 'contains': ['72.bc1.a1', '72.bf1.a1', '72.bk1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7838, -1, 6718, -1, 7274, -1, 7675, -1], 'generators': [589, 6], 'label': '1152.155799.36.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bi1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968246
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '36.bj1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.br1.a1', '18.d1.a1', '18.i1.a1', '18.n1.a1'], 'contains': ['72.bd1.a1', '72.bf1.a1', '72.bj1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6242, -1, 6495, -1, 7152, -1, 7171, -1], 'generators': [13, 582], 'label': '1152.155799.36.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bj1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968247
    {'ambient': '1152.155799', 'aut_centralizer_order': 2, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '768.1083444', 'aut_weyl_index': 6, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.l1.a1', '12.o1.a1', '12.q1.a1', '12.bf1.a1', '12.bg1.a1', '12.bj1.a1', '12.bk1.a1', '18.b1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6747, -1, 7169, -1, 5851, -1, 6450, -1], 'generators': [1, 48, 576, 2, 384, 108, 600], 'label': '1152.155799.6.g1.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': '6.g1.a1', 'projective_image': '576.8312', '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': '96.209'}
  • id: 60968248
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '36.bk1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bs1.a1', '18.d1.a1', '18.h1.a1', '18.o1.a1'], 'contains': ['72.be1.a1', '72.bf1.a1', '72.bh1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6191, -1, 6336, -1, 6991, -1, 6937, -1], 'generators': [99, 12], 'label': '1152.155799.36.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bk1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968249
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '36.bl1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bt1.a1', '18.c1.a1', '18.i1.a1', '18.o1.a1'], 'contains': ['72.bf1.a1', '72.bg1.a1', '72.bi1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7527, -1, 7812, -1, 6950, -1, 7636, -1], 'generators': [99, 108], 'label': '1152.155799.36.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bl1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968250
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '36.bm1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bu1.a1', '12.bw1.a1', '18.e1.a1'], 'contains': ['72.u1.a1', '72.w1.a1', '72.z1.a1', '72.bn1.a1', '72.bs1.a1', '72.bt1.a1', '72.bu1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1834, -1, 2586, -1, 1854, -1, 2351, -1], 'generators': [25, 2, 96], 'label': '1152.155799.36.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '36.bm1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60968251
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '36.bn1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.bv1.a1', '18.e1.a1', '18.l1.a1', '18.m1.a1'], 'contains': ['72.a1.a1', '72.v1.a1', '72.x1.a1', '72.bb1.a1', '72.bs1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5240, -1, 4391, -1, 5007, -1, 4940, -1], 'generators': [2, 24, 96], 'label': '1152.155799.36.bn1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.bn1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968252
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '36.bo1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bx1.a1', '12.by1.a1', '12.bz1.a1', '18.e1.a1', '18.n1.a1', '18.o1.a1'], 'contains': ['72.a1.a1', '72.y1.a1', '72.ba1.a1', '72.bf1.a1', '72.bt1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4252, -1, 5520, -1, 4536, -1, 4539, -1], 'generators': [3, 24, 96], 'label': '1152.155799.36.bo1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bo1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968253
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '36.bp1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.ca1.a1', '18.f1.a1', '18.l1.a1', '18.n1.a1'], 'contains': ['72.a1.a1', '72.bc1.a1', '72.bd1.a1', '72.bl1.a1', '72.bv1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5421, -1, 5830, -1, 6331, -1, 6674, -1], 'generators': [6, 24, 576], 'label': '1152.155799.36.bp1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.bp1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968254
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '36.bq1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cb1.a1', '12.cd1.a1', '12.cg1.a1', '18.f1.a1', '18.m1.a1', '18.o1.a1'], 'contains': ['72.a1.a1', '72.be1.a1', '72.bg1.a1', '72.bm1.a1', '72.bw1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5361, -1, 5412, -1, 5921, -1, 6039, -1], 'generators': [7, 24, 576], 'label': '1152.155799.36.bq1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bq1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968255
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '36.br1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.ce1.a1', '18.g1.a1', '18.m1.a1', '18.n1.a1'], 'contains': ['72.a1.a1', '72.bj1.a1', '72.bk1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5851, -1, 6045, -1, 7881, -1, 7435, -1], 'generators': [13, 96, 576], 'label': '1152.155799.36.br1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.br1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.br1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968256
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '36.bs1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cc1.a1', '12.cf1.a1', '18.f1.a1'], 'contains': ['72.bo1.a1', '72.bp1.a1', '72.bq1.a1', '72.br1.a1', '72.bu1.a1', '72.bv1.a1', '72.bw1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3358, -1, 2839, -1, 3551, -1, 5250, -1], 'generators': [25, 6, 576], 'label': '1152.155799.36.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '36.bs1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60968257
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '36.bt1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ci1.a1', '18.a1.a1'], 'contains': ['72.bx1.a1', '72.bz1.a1', '72.ca1.a1', '72.ce1.a1', '72.ch1.a1', '72.cj1.a1', '72.ck1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9443, -1, 9521, -1, 9291, -1, 9590, -1], 'generators': [577, 2, 12], 'label': '1152.155799.36.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.bt1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60968258
    {'ambient': '1152.155799', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2304.oh', 'aut_weyl_index': 2, 'centralizer': '576.a1.a1', 'complements': ['576.f1.a1', '576.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.d1.a1', '4.e1.a1', '4.i1.a1', '4.l1.a1', '6.d1.a1', '6.k1.a1', '8.e1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3236, 2533, 4418, 6438, 5018, 2124, 3400, 4475], 'generators': [1, 32, 384, 6, 48, 576, 96, 24], 'label': '1152.155799.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.d1.a1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '576.8312', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '576.8312'}
  • id: 60968259
    {'ambient': '1152.155799', 'aut_centralizer_order': 2, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '768.1083444', 'aut_weyl_index': 6, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.m1.a1', '12.n1.a1', '12.q1.a1', '12.bm1.a1', '12.bp1.a1', '12.bq1.a1', '12.bt1.a1', '18.c1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7852, -1, 7793, -1, 5998, -1, 7689, -1], 'generators': [1, 48, 576, 98, 384, 108, 600], 'label': '1152.155799.6.h1.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': '6.h1.a1', 'projective_image': '576.8312', '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': '96.209'}
  • id: 60968260
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '36.bu1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.46', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cj1.a1', '18.a1.a1'], 'contains': ['72.bx1.a1', '72.bz1.a1', '72.cb1.a1', '72.cf1.a1', '72.cg1.a1', '72.ci1.a1', '72.cl1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9635, -1, 9358, -1, 9388, -1, 9749, -1], 'generators': [577, 2, 588], 'label': '1152.155799.36.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.bu1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60968261
    {'ambient': '1152.155799', 'aut_centralizer_order': 192, 'aut_label': '48.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '12.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.b1.a1', '24.k1.a1', '24.p1.a1', '24.r1.a1', '24.s1.a1'], 'contains': ['96.a1.a1', '96.b1.a1', '96.c1.a1', '144.e1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7913, 6857, 8326, 4211, 5886, 6475, 6910, 4178], 'generators': [1, 24, 48, 384], 'label': '1152.155799.48.a1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['12.a1.a1', '24.b1.a1'], 'normal_contains': ['96.a1.a1', '96.b1.a1', '96.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968262
    {'ambient': '1152.155799', 'aut_centralizer_order': 384, 'aut_label': '48.b1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '12.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.c1.a1', '24.d1.a1', '24.by1.a1', '24.ca1.a1', '24.cd1.a1', '24.ce1.a1'], 'contains': ['96.d1.a1', '96.g1.a1', '96.bb1.a1', '144.a1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1863, 3898, 2324, 3068, 1239, 4033, 2129, 3197], 'generators': [48, 96, 576, 384], 'label': '1152.155799.48.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1', '24.c1.a1', '24.d1.a1'], 'normal_contains': ['96.d1.a1', '144.a1.a1', '192.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '576.8312', 'quotient_action_image': '12.4', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968263
    {'ambient': '1152.155799', 'aut_centralizer_order': 192, 'aut_label': '48.c1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.e1.a1', '24.f1.a1', '24.bz1.a1', '24.cb1.a1', '24.cf1.a1', '24.cg1.a1', '24.ch1.a1'], 'contains': ['96.e1.a1', '144.a1.a1', '192.c1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [807, 2617, 841, 5047, 2011, 3094, 1756, 5589], 'generators': [48, 32, 96, 576], 'label': '1152.155799.48.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.c1.a1', 'normal_contained_in': ['16.a1.a1', '24.e1.a1'], 'normal_contains': ['96.e1.a1', '144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.c1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60968264
    {'ambient': '1152.155799', 'aut_centralizer_order': 576, 'aut_label': '48.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '4.f1.a1', 'complements': ['24.de1.a1', '24.de1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '24.b1.a1', '24.bn1.a1', '24.cn1.a1', '24.cr1.a1', '24.cz1.a1'], 'contains': ['96.b1.a1', '144.b1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7035, 9006, 7551, 6543, 8713, 8634, 8157, 6182], 'generators': [12, 384, 24, 48], 'label': '1152.155799.48.d1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.d1.a1', 'normal_contained_in': ['12.c1.a1', '24.b1.a1'], 'normal_contains': ['96.b1.a1', '144.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.d1.a1', 'projective_image': '576.8312', 'quotient_action_image': '4.2', 'quotient_action_kernel': '12.3', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968265
    {'ambient': '1152.155799', 'aut_centralizer_order': 192, 'aut_label': '48.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '12.f1.a1', 'complements': ['24.de1.a1', '24.de1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '24.b1.a1', '24.bp1.a1', '24.co1.a1', '24.ct1.a1', '24.cx1.a1'], 'contains': ['96.b1.a1', '144.bi1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8388, 8382, 8923, 5752, 8796, 8056, 8550, 4783], 'generators': [13, 24, 48, 384], 'label': '1152.155799.48.e1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.e1.a1', 'normal_contained_in': ['12.d1.a1', '24.b1.a1'], 'normal_contains': ['96.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.e1.a1', 'projective_image': '576.8312', 'quotient_action_image': '4.2', 'quotient_action_kernel': '12.3', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '48.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968266
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '48.f1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '36.10', 'aut_weyl_index': 128, 'centralizer': '36.a1.a1', 'complements': ['24.cv1.a1', '24.dc1.a1', '24.dd1.a1', '24.cw1.a1', '24.db1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.a1.a1', '24.dg1.a1'], 'contains': ['96.d1.a1', '96.y1.a1', '96.bc1.a1', '144.br1.a1'], 'core': '48.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [561, 1604, 605, 426, 486, 2156, 1144, 1649], 'generators': [1, 96, 576, 384], 'label': '1152.155799.48.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.f1.a1', 'normal_contained_in': ['16.b1.a1', '24.a1.a1'], 'normal_contains': ['96.d1.a1', '192.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.f1.a1', 'projective_image': '1152.155799', 'quotient_action_image': '6.1', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '48.f1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 60968267
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '48.f1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '36.10', 'aut_weyl_index': 128, 'centralizer': '36.a1.a1', 'complements': ['24.cv1.a1', '24.dc1.a1', '24.dd1.a1', '24.cw1.a1', '24.db1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b1', '24.a1.a1', '24.dg1.b1'], 'contains': ['96.d1.a1', '96.y1.b1', '96.bc1.b1', '144.br1.b1'], 'core': '48.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [561, 1604, 967, 1861, 486, 2156, 655, 822], 'generators': [49, 96, 576, 384], 'label': '1152.155799.48.f1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.f1.b1', 'normal_contained_in': ['16.b1.b1', '24.a1.a1'], 'normal_contains': ['96.d1.a1', '192.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '48.f1.b1', 'projective_image': '1152.155799', 'quotient_action_image': '6.1', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '48.f1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 60968268
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '16.c1.a1', '24.g1.a1'], 'contains': ['96.f1.a1', '96.j1.a1', '96.l1.a1', '96.x1.a1', '96.x1.b1', '144.d1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [639, -1, 895, -1, 2473, -1, 1548, -1], 'generators': [1, 2, 48, 32], 'label': '1152.155799.48.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.g1.a1', 'old_label': '48.g1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968269
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '24.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '16.d1.a1', '24.g1.a1', '24.h1.a1', '24.i1.a1'], 'contains': ['96.f1.a1', '96.r1.a1', '96.s1.a1', '144.e1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2034, -1, 2694, -1, 5820, -1, 3370, -1], 'generators': [1, 24, 32, 48], 'label': '1152.155799.48.h1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '48.h1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968270
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.m1.a1', '12.o1.a1', '12.p1.a1', '12.bn1.a1', '12.bo1.a1', '12.br1.a1', '12.bs1.a1', '18.d1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6217, -1, 6670, -1, 5924, -1, 6380, -1], 'generators': [1, 48, 576, 98, 384, 12, 24], 'label': '1152.155799.6.i1.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': '6.i1.a1', 'projective_image': '576.8312', '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': '96.209'}
  • id: 60968271
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '16.e1.a1', '24.h1.a1'], 'contains': ['96.f1.a1', '96.t1.a1', '96.u1.a1', '144.g1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1588, -1, 2151, -1, 4739, -1, 3456, -1], 'generators': [1, 6, 48, 32], 'label': '1152.155799.48.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.h1.a1', 'old_label': '48.i1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968272
    {'ambient': '1152.155799', 'aut_centralizer_order': 128, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '18.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.j1.a1', '24.k1.a1', '24.l1.a1', '24.m1.a1', '24.n1.a1', '24.o1.a1'], 'contains': ['96.a1.a1', '96.g1.a1', '96.h1.a1', '96.y1.a1', '96.y1.b1', '96.z1.a1', '96.z1.b1', '144.c1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3852, -1, 3905, -1, 2092, -1, 3616, -1], 'generators': [1, 48, 96, 384], 'label': '1152.155799.48.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.j1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968273
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.j1.a1', '24.p1.a1', '24.q1.a1'], 'contains': ['96.a1.a1', '96.i1.a1', '96.k1.a1', '96.ba1.a1', '96.ba1.b1', '144.d1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5545, -1, 6338, -1, 2863, -1, 2686, -1], 'generators': [1, 2, 48, 384], 'label': '1152.155799.48.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1.a1', 'old_label': '48.k1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968274
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '24.l1.a1', '24.q1.a1', '24.t1.a1'], 'contains': ['96.a1.a1', '96.n1.a1', '96.o1.a1', '144.f1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8140, -1, 8276, -1, 4603, -1, 5573, -1], 'generators': [1, 120, 48, 384], 'label': '1152.155799.48.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.l1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968275
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '144.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '24.n1.a1', '24.r1.a1', '24.t1.a1'], 'contains': ['96.a1.a1', '96.p1.a1', '96.q1.a1', '144.g1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8924, -1, 8748, -1, 5126, -1, 6659, -1], 'generators': [1, 6, 48, 384], 'label': '1152.155799.48.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '48.m1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968276
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.u1.a1', '24.v1.a1', '24.w1.a1', '24.x1.a1', '24.y1.a1', '24.z1.a1'], 'contains': ['96.g1.a1', '96.h1.a1', '96.bc1.a1', '96.bc1.b1', '96.bi1.a1', '144.h1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3423, -1, 3848, -1, 1772, -1, 2975, -1], 'generators': [577, 48, 96, 384], 'label': '1152.155799.48.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.n1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968277
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '48.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '24.u1.a1', '24.ba1.a1', '24.bb1.a1', '24.bc1.a1', '24.bd1.a1', '24.by1.a1'], 'contains': ['96.g1.a1', '96.i1.a1', '96.bd1.a1', '96.bj1.a1', '144.i1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3035, -1, 3330, -1, 1642, -1, 2892, -1], 'generators': [2, 48, 576, 384], 'label': '1152.155799.48.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '48.o1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60968294
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '48.bd1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '24.x1.a1', '24.cl1.a1', '24.cq1.a1'], 'contains': ['96.c1.a1', '96.h1.a1', '96.n1.a1', '144.w1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8032, -1, 8376, -1, 4544, -1, 5515, -1], 'generators': [97, 120, 48, 384], 'label': '1152.155799.48.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.bd1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968278
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '24.v1.a1', '24.ba1.a1', '24.be1.a1', '24.bf1.a1', '24.bg1.a1', '24.ca1.a1'], 'contains': ['96.g1.a1', '96.k1.a1', '96.be1.a1', '96.bk1.a1', '144.j1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2805, -1, 3389, -1, 1573, -1, 2826, -1], 'generators': [3, 48, 576, 384], 'label': '1152.155799.48.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '48.p1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.p1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60968279
    {'ambient': '1152.155799', 'aut_centralizer_order': 384, 'aut_label': '48.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.k1.a1', '24.w1.a1', '24.bd1.a1', '24.bg1.a1', '24.bh1.a1', '24.bi1.a1', '24.bj1.a1', '24.bk1.a1', '24.bl1.a1', '24.bm1.a1', '24.bn1.a1', '24.bo1.a1', '24.bp1.a1', '24.bq1.a1'], 'contains': ['96.b1.a1', '96.g1.a1', '96.n1.a1', '144.k1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7327, -1, 7747, -1, 5559, -1, 6451, -1], 'generators': [24, 96, 384, 48], 'label': '1152.155799.48.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.q1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.q1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968280
    {'ambient': '1152.155799', 'aut_centralizer_order': 192, 'aut_label': '48.r1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.l1.a1', '24.x1.a1', '24.bb1.a1', '24.be1.a1', '24.br1.a1', '24.bs1.a1'], 'contains': ['96.g1.a1', '96.n1.a1', '144.l1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4072, -1, 4103, -1, 3100, -1, 4824, -1], 'generators': [600, 96, 384, 48], 'label': '1152.155799.48.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.r1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.r1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968281
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '6.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.a1'], 'contains': ['12.a1.a1', '12.k1.a1', '12.l1.a1', '12.m1.a1', '12.s1.a1', '12.w1.a1', '12.x1.a1', '12.y1.a1', '12.bu1.a1', '12.bv1.a1', '12.bx1.a1', '18.e1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3777, -1, 4797, -1, 4269, -1, 4091, -1], 'generators': [1, 576, 48, 2, 384, 24, 96], 'label': '1152.155799.6.j1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.j1.a1', 'projective_image': '576.8312', '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': '96.209'}
  • id: 60968282
    {'ambient': '1152.155799', 'aut_centralizer_order': 128, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.k1.a1', '24.x1.a1', '24.ba1.a1', '24.bt1.a1', '24.bu1.a1', '24.bv1.a1'], 'contains': ['96.c1.a1', '96.g1.a1', '96.o1.a1', '144.m1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3712, -1, 3965, -1, 3011, -1, 4894, -1], 'generators': [25, 96, 48, 384], 'label': '1152.155799.48.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.s1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968283
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '48.t1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.l1.a1', '24.w1.a1', '24.bc1.a1', '24.bf1.a1', '24.bw1.a1', '24.bx1.a1'], 'contains': ['96.g1.a1', '96.o1.a1', '144.n1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4007, -1, 4041, -1, 2604, -1, 4754, -1], 'generators': [601, 96, 48, 384], 'label': '1152.155799.48.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.t1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.t1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968284
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '48.u1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '48.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '24.v1.a1', '24.bb1.a1', '24.bf1.a1', '24.bh1.a1', '24.bt1.a1', '24.by1.a1'], 'contains': ['96.g1.a1', '96.bf1.a1', '144.o1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2615, -1, 3065, -1, 1443, -1, 2358, -1], 'generators': [98, 48, 384, 576], 'label': '1152.155799.48.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '48.u1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.u1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60968285
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '48.v1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '24.y1.a1', '24.bi1.a1', '24.br1.a1', '24.bu1.a1', '24.bw1.a1', '24.cd1.a1'], 'contains': ['96.g1.a1', '96.p1.a1', '144.p1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5158, -1, 5002, -1, 3929, -1, 5958, -1], 'generators': [6, 96, 384, 48], 'label': '1152.155799.48.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '48.v1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.v1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60968286
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '48.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '48.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '24.z1.a1', '24.bj1.a1', '24.br1.a1', '24.bv1.a1', '24.bx1.a1', '24.cd1.a1'], 'contains': ['96.g1.a1', '96.bl1.a1', '144.q1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4815, -1, 4739, -1, 3358, -1, 5082, -1], 'generators': [582, 96, 384, 144], 'label': '1152.155799.48.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '48.w1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.w1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60968287
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '48.x1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '144.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '24.y1.a1', '24.bk1.a1', '24.bs1.a1', '24.bv1.a1', '24.bw1.a1', '24.ce1.a1'], 'contains': ['96.g1.a1', '96.bm1.a1', '144.r1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4666, -1, 4577, -1, 3212, -1, 5012, -1], 'generators': [583, 96, 144, 384], 'label': '1152.155799.48.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '48.x1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.x1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60968288
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '48.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '144.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '24.u1.a1', '24.bc1.a1', '24.be1.a1', '24.bl1.a1', '24.bt1.a1', '24.ca1.a1'], 'contains': ['96.g1.a1', '96.bg1.a1', '144.s1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2549, -1, 3126, -1, 1370, -1, 2486, -1], 'generators': [99, 48, 576, 384], 'label': '1152.155799.48.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '48.y1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.y1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60968289
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '48.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '144.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '24.z1.a1', '24.bm1.a1', '24.bs1.a1', '24.bu1.a1', '24.bx1.a1', '24.ce1.a1'], 'contains': ['96.g1.a1', '96.q1.a1', '144.t1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5077, -1, 4800, -1, 3856, -1, 5849, -1], 'generators': [7, 96, 48, 384], 'label': '1152.155799.48.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '48.z1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.z1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60968290
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '48.ba1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.cc1.a1', '24.ci1.a1', '24.cj1.a1'], 'contains': ['96.bh1.a1', '144.a1.a1', '192.d1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2190, -1, 2470, -1, 1080, -1, 1916, -1], 'generators': [48, 416, 96, 576], 'label': '1152.155799.48.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '48.ba1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60968291
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '48.bb1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '24.ck1.a1', '24.cl1.a1'], 'contains': ['96.h1.a1', '96.i1.a1', '96.k1.a1', '96.bn1.a1', '96.bn1.b1', '144.u1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7677, -1, 7611, -1, 3428, -1, 3255, -1], 'generators': [577, 2, 48, 384], 'label': '1152.155799.48.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1.a1', 'old_label': '48.bb1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968292
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '6.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.b1.a1'], 'contains': ['12.a1.a1', '12.n1.a1', '12.o1.a1', '12.r1.a1', '12.t1.a1', '12.z1.a1', '12.ba1.a1', '12.bd1.a1', '12.ca1.a1', '12.cb1.a1', '12.cc1.a1', '18.f1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4920, -1, 5214, -1, 4844, -1, 5755, -1], 'generators': [1, 96, 48, 6, 384, 24, 576], 'label': '1152.155799.6.k1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.k1.a1', 'projective_image': '576.8312', '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': '96.209'}
  • id: 60968293
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '48.bc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '24.w1.a1', '24.ck1.a1', '24.cm1.a1', '24.cn1.a1', '24.co1.a1', '24.cp1.a1'], 'contains': ['96.b1.a1', '96.h1.a1', '96.o1.a1', '144.v1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8781, -1, 9753, -1, 6297, -1, 7131, -1], 'generators': [97, 24, 48, 384], 'label': '1152.155799.48.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.bc1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968296
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '48.bf1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '144.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '24.cm1.a1', '24.cq1.a1'], 'contains': ['96.h1.a1', '96.p1.a1', '96.q1.a1', '144.y1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9847, -1, 9197, -1, 5226, -1, 6755, -1], 'generators': [97, 6, 48, 384], 'label': '1152.155799.48.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '48.bf1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968297
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '48.bg1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '24.p1.a1', '24.ba1.a1', '24.cl1.a1'], 'contains': ['96.c1.a1', '96.i1.a1', '96.k1.a1', '144.z1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5496, -1, 5838, -1, 3483, -1, 3814, -1], 'generators': [25, 2, 48, 384], 'label': '1152.155799.48.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1.a1', 'old_label': '48.bg1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60968298
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '48.bh1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '24.ba1.a1', '24.ck1.a1'], 'contains': ['96.i1.a1', '96.k1.a1', '96.o1.a1', '144.ba1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7868, -1, 7671, -1, 3985, -1, 4157, -1], 'generators': [601, 2, 48, 384], 'label': '1152.155799.48.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1.a1', 'old_label': '48.bh1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60968299
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '48.bi1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '96.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '24.p1.a1', '24.bd1.a1', '24.ck1.a1', '24.cr1.a1', '24.cs1.a1', '24.ct1.a1', '24.cu1.a1'], 'contains': ['96.b1.a1', '96.i1.a1', '144.bb1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8712, -1, 8169, -1, 6528, -1, 7074, -1], 'generators': [2, 24, 384, 48], 'label': '1152.155799.48.bi1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '48.bi1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968300
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '48.bj1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '96.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '24.bd1.a1', '24.cl1.a1'], 'contains': ['96.i1.a1', '96.n1.a1', '144.bc1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8086, -1, 7957, -1, 4886, -1, 4473, -1], 'generators': [2, 600, 384, 48], 'label': '1152.155799.48.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '48.bj1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968301
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '48.bk1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bw1.a1', '16.f1.a1', '24.g1.a1'], 'contains': ['96.j1.a1', '96.l1.a1', '96.s1.a1', '144.z1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [702, -1, 1042, -1, 3156, -1, 2305, -1], 'generators': [25, 2, 48, 32], 'label': '1152.155799.48.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.g1.a1', 'old_label': '48.bk1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968302
    {'ambient': '1152.155799', 'aut_centralizer_order': 24, 'aut_label': '48.bl1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '16.g1.a1', '24.g1.a1', '24.cv1.a1', '24.cw1.a1'], 'contains': ['96.j1.a1', '96.r1.a1', '144.bb1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2280, -1, 3773, -1, 6677, -1, 3510, -1], 'generators': [2, 24, 48, 32], 'label': '1152.155799.48.bl1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '48.bl1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
  • id: 60968303
    {'ambient': '1152.155799', 'aut_centralizer_order': 2, 'aut_label': '6.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '768.1083444', 'aut_weyl_index': 6, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.x1.a1', '12.z1.a1', '12.bb1.a1', '12.be1.a1', '12.bg1.a1', '12.bq1.a1', '12.bs1.a1', '18.h1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7385, -1, 7056, -1, 6317, -1, 6811, -1], 'generators': [97, 48, 576, 2, 384, 12, 24], 'label': '1152.155799.6.l1.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': '6.l1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.l1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968304
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '48.bm1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '24.p1.a1', '24.bg1.a1', '24.ck1.a1', '24.cx1.a1', '24.cy1.a1', '24.cz1.a1', '24.da1.a1'], 'contains': ['96.b1.a1', '96.k1.a1', '144.bd1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8560, -1, 8956, -1, 6407, -1, 7026, -1], 'generators': [3, 24, 48, 384], 'label': '1152.155799.48.bm1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '48.bm1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60968305
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '48.bn1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '24.bg1.a1', '24.cl1.a1'], 'contains': ['96.k1.a1', '96.n1.a1', '144.be1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7741, -1, 8084, -1, 4836, -1, 4309, -1], 'generators': [3, 600, 48, 384], 'label': '1152.155799.48.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '48.bn1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60968306
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '48.bo1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.by1.a1', '16.h1.a1', '24.g1.a1', '24.db1.a1', '24.dc1.a1'], 'contains': ['96.l1.a1', '96.r1.a1', '144.bd1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3236, -1, 4226, -1, 6638, -1, 3564, -1], 'generators': [3, 24, 48, 32], 'label': '1152.155799.48.bo1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '48.bo1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
  • id: 60968307
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '48.bp1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bz1.a1', '16.h1.a1', '24.dd1.a1'], 'contains': ['96.m1.a1', '96.v1.a1', '144.bd1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3928, -1, 5411, -1, 5333, -1, 4102, -1], 'generators': [3, 24, 48, 416], 'label': '1152.155799.48.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.dd1.a1', 'old_label': '48.bp1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
  • id: 60968308
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '48.bq1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '96.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '24.r1.a1', '24.bi1.a1', '24.cm1.a1', '24.cr1.a1', '24.cs1.a1', '24.cx1.a1', '24.cy1.a1'], 'contains': ['96.b1.a1', '96.p1.a1', '144.bf1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9701, -1, 9013, -1, 7273, -1, 8084, -1], 'generators': [6, 24, 384, 48], 'label': '1152.155799.48.bq1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '48.bq1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968309
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '48.br1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '24.r1.a1', '24.bm1.a1', '24.cm1.a1', '24.ct1.a1', '24.cu1.a1', '24.cz1.a1', '24.da1.a1'], 'contains': ['96.b1.a1', '96.q1.a1', '144.bg1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9049, -1, 9056, -1, 6895, -1, 8011, -1], 'generators': [7, 24, 48, 384], 'label': '1152.155799.48.br1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '48.br1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.br1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60968310
    {'ambient': '1152.155799', 'aut_centralizer_order': 192, 'aut_label': '48.bs1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.a1', '24.bn1.a1', '24.bo1.a1', '24.co1.a1', '24.cp1.a1', '24.cs1.a1', '24.da1.a1'], 'contains': ['96.b1.a1', '144.bh1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8968, -1, 9894, -1, 7224, -1, 9059, -1], 'generators': [108, 384, 24, 48], 'label': '1152.155799.48.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.bs1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968311
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '48.bt1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.a1', '24.bp1.a1', '24.bq1.a1', '24.cn1.a1', '24.cp1.a1', '24.cu1.a1', '24.cy1.a1'], 'contains': ['96.b1.a1', '144.bj1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8863, -1, 9979, -1, 7184, -1, 9097, -1], 'generators': [109, 24, 48, 384], 'label': '1152.155799.48.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.bt1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968312
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '48.bu1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '96.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.a1', '24.bi1.a1', '24.cq1.a1'], 'contains': ['96.n1.a1', '96.p1.a1', '144.bk1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9974, -1, 9625, -1, 5493, -1, 7286, -1], 'generators': [6, 120, 384, 48], 'label': '1152.155799.48.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '48.bu1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968313
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '48.bv1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.a1', '24.bm1.a1', '24.cq1.a1'], 'contains': ['96.n1.a1', '96.q1.a1', '144.bl1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9928, -1, 9582, -1, 5442, -1, 7237, -1], 'generators': [7, 120, 48, 384], 'label': '1152.155799.48.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '48.bv1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60968314
    {'ambient': '1152.155799', 'aut_centralizer_order': 2, 'aut_label': '6.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '768.1083444', 'aut_weyl_index': 6, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.x1.a1', '12.ba1.a1', '12.bc1.a1', '12.bf1.a1', '12.bh1.a1', '12.br1.a1', '12.bt1.a1', '18.i1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6822, -1, 7452, -1, 6061, -1, 7190, -1], 'generators': [97, 48, 576, 2, 384, 108, 600], 'label': '1152.155799.6.m1.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': '6.m1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.m1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968315
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '48.bw1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '24.r1.a1', '24.bu1.a1', '24.cq1.a1'], 'contains': ['96.c1.a1', '96.p1.a1', '96.q1.a1', '144.bm1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8826, -1, 8790, -1, 5176, -1, 6707, -1], 'generators': [25, 6, 48, 384], 'label': '1152.155799.48.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '48.bw1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60968316
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '48.bx1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.a1', '24.bu1.a1', '24.cm1.a1'], 'contains': ['96.o1.a1', '96.p1.a1', '96.q1.a1', '144.bn1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9892, -1, 9682, -1, 5276, -1, 6861, -1], 'generators': [121, 6, 48, 384], 'label': '1152.155799.48.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '48.bx1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60968317
    {'ambient': '1152.155799', 'aut_centralizer_order': 24, 'aut_label': '48.by1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '16.i1.a1', '24.h1.a1', '24.cv1.a1', '24.db1.a1'], 'contains': ['96.r1.a1', '96.t1.a1', '144.bf1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2362, -1, 5176, -1, 8837, -1, 4064, -1], 'generators': [6, 24, 48, 32], 'label': '1152.155799.48.by1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '48.by1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.by1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
  • id: 60968318
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '48.bz1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cd1.a1', '16.j1.a1', '24.h1.a1', '24.cw1.a1', '24.dc1.a1'], 'contains': ['96.r1.a1', '96.u1.a1', '144.bg1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3288, -1, 4192, -1, 7384, -1, 4025, -1], 'generators': [7, 24, 48, 32], 'label': '1152.155799.48.bz1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '48.bz1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
  • id: 60968319
    {'ambient': '1152.155799', 'aut_centralizer_order': 144, 'aut_label': '48.ca1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '16.k1.a1', '24.i1.a1', '24.cv1.a1', '24.dc1.a1'], 'contains': ['96.r1.a1', '144.b1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4207, -1, 5588, -1, 9605, -1, 4234, -1], 'generators': [12, 32, 24, 48], 'label': '1152.155799.48.ca1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '48.ca1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968320
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '48.cb1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '24.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ce1.a1', '16.l1.a1', '24.i1.a1', '24.cw1.a1', '24.db1.a1'], 'contains': ['96.r1.a1', '144.bi1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4377, -1, 5472, -1, 9832, -1, 4271, -1], 'generators': [13, 32, 24, 48], 'label': '1152.155799.48.cb1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '48.cb1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968321
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '48.cc1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cf1.a1', '16.m1.a1', '24.h1.a1'], 'contains': ['96.s1.a1', '96.t1.a1', '96.u1.a1', '144.bm1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2099, -1, 2414, -1, 4796, -1, 3853, -1], 'generators': [25, 6, 48, 32], 'label': '1152.155799.48.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.h1.a1', 'old_label': '48.cc1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968322
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '48.cd1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.38', 'aut_weyl_index': 96, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cg1.a1', '16.j1.a1', '24.dd1.a1'], 'contains': ['96.v1.a1', '96.w1.a1', '144.bg1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [4412, -1, 5312, -1, 5936, -1, 4196, -1], 'generators': [7, 24, 48, 416], 'label': '1152.155799.48.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.dd1.a1', 'old_label': '48.cd1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
  • id: 60968323
    {'ambient': '1152.155799', 'aut_centralizer_order': 72, 'aut_label': '48.ce1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ch1.a1', '16.k1.a1', '24.dd1.a1'], 'contains': ['96.v1.a1', '144.b1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4464, -1, 5621, -1, 6995, -1, 4701, -1], 'generators': [12, 416, 24, 48], 'label': '1152.155799.48.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.n1.a1', 'old_label': '48.ce1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968324
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '48.cf1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '72.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.f1.a1', '24.de1.a1'], 'contains': ['96.e1.a1', '144.br1.a1', '192.e1.a1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [126, -1, 21, -1, 422, -1, 381, -1], 'generators': [1, 32, 96, 576], 'label': '1152.155799.48.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.cf1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60968325
    {'ambient': '1152.155799', 'aut_centralizer_order': 2, 'aut_label': '6.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '768.1083444', 'aut_weyl_index': 6, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.y1.a1', '12.z1.a1', '12.bc1.a1', '12.bi1.a1', '12.bk1.a1', '12.bm1.a1', '12.bo1.a1', '18.j1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7551, -1, 7596, -1, 6216, -1, 6909, -1], 'generators': [97, 48, 576, 98, 384, 108, 600], 'label': '1152.155799.6.n1.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': '6.n1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.n1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968326
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '48.cf1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '72.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b1', '24.f1.a1', '24.de1.b1'], 'contains': ['96.e1.a1', '144.br1.b1', '192.e1.b1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [126, -1, 241, -1, 422, -1, 25, -1], 'generators': [49, 32, 96, 576], 'label': '1152.155799.48.cf1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.cf1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cf1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60968327
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '48.cg1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.df1.a1'], 'contains': ['96.y1.a1', '96.z1.a1', '96.bb1.a1', '96.bc1.b1', '96.bi1.a1', '144.bo1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1373, -1, 1766, -1, 895, -1, 1466, -1], 'generators': [1, 624, 96, 384], 'label': '1152.155799.48.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.cg1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968328
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '48.cg1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.df1.b1'], 'contains': ['96.y1.b1', '96.z1.b1', '96.bb1.a1', '96.bc1.a1', '96.bi1.a1', '144.bo1.b1'], 'core': '192.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [1373, -1, 1918, -1, 895, -1, 1400, -1], 'generators': [577, 624, 96, 384], 'label': '1152.155799.48.cg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.cg1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cg1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968329
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '48.ch1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '24.df1.a1', '24.dg1.a1'], 'contains': ['96.y1.a1', '96.ba1.a1', '96.bd1.a1', '96.be1.a1', '96.bn1.a1', '144.bp1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1280, -1, 1510, -1, 826, -1, 1334, -1], 'generators': [1, 2, 576, 384], 'label': '1152.155799.48.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '48.ch1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968330
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '48.ch1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '24.df1.b1', '24.dg1.b1'], 'contains': ['96.y1.b1', '96.ba1.b1', '96.bd1.a1', '96.be1.a1', '96.bn1.b1', '144.bp1.b1'], 'core': '192.b1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [1280, -1, 1824, -1, 826, -1, 1268, -1], 'generators': [49, 2, 576, 384], 'label': '1152.155799.48.ch1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '48.ch1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ch1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968331
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '48.ci1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '144.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '24.df1.a1', '24.dg1.a1'], 'contains': ['96.y1.a1', '96.bf1.a1', '96.bg1.a1', '144.bq1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [907, -1, 1306, -1, 550, -1, 774, -1], 'generators': [1, 98, 576, 384], 'label': '1152.155799.48.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '48.ci1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968332
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '48.ci1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '144.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '24.df1.b1', '24.dg1.b1'], 'contains': ['96.y1.b1', '96.bf1.a1', '96.bg1.a1', '144.bq1.b1'], 'core': '192.b1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [907, -1, 1424, -1, 550, -1, 717, -1], 'generators': [49, 98, 576, 384], 'label': '1152.155799.48.ci1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '48.ci1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ci1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968333
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '48.cj1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1'], 'contains': ['96.z1.a1', '96.ba1.a1', '96.bj1.a1', '96.bk1.a1', '96.bn1.b1', '144.bs1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2912, -1, 3187, -1, 1016, -1, 2554, -1], 'generators': [1, 2, 624, 384], 'label': '1152.155799.48.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.k1.a1', 'old_label': '48.cj1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968334
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '48.cj1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1'], 'contains': ['96.z1.b1', '96.ba1.b1', '96.bj1.a1', '96.bk1.a1', '96.bn1.a1', '144.bs1.b1'], 'core': '192.b1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [2912, -1, 3258, -1, 1016, -1, 2620, -1], 'generators': [577, 2, 624, 384], 'label': '1152.155799.48.cj1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.k1.a1', 'old_label': '48.cj1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cj1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968335
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '48.ck1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '144.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1'], 'contains': ['96.z1.a1', '96.bl1.a1', '96.bm1.a1', '144.bt1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4725, -1, 4683, -1, 2730, -1, 4530, -1], 'generators': [1, 582, 144, 384], 'label': '1152.155799.48.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.r1.a1', 'old_label': '48.ck1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968336
    {'ambient': '1152.155799', 'aut_centralizer_order': 2, 'aut_label': '6.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '768.1083444', 'aut_weyl_index': 6, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['12.y1.a1', '12.ba1.a1', '12.bb1.a1', '12.bj1.a1', '12.bl1.a1', '12.bn1.a1', '12.bp1.a1', '18.k1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6535, -1, 7681, -1, 6629, -1, 7005, -1], 'generators': [97, 48, 576, 98, 384, 12, 24], 'label': '1152.155799.6.o1.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': '6.o1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.o1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968337
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '48.ck1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '144.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1'], 'contains': ['96.z1.b1', '96.bl1.a1', '96.bm1.a1', '144.bt1.b1'], 'core': '192.b1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [4725, -1, 4633, -1, 2730, -1, 4587, -1], 'generators': [97, 582, 144, 384], 'label': '1152.155799.48.ck1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.r1.a1', 'old_label': '48.ck1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ck1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968338
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '48.cl1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '96.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.by1.a1', '24.df1.a1', '24.df1.b1'], 'contains': ['96.bb1.a1', '96.bd1.a1', '96.bf1.a1', '144.bu1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1185, -1, 1647, -1, 651, -1, 1206, -1], 'generators': [2, 144, 384, 576], 'label': '1152.155799.48.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '48.cl1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60968339
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '48.cm1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ca1.a1', '24.df1.a1', '24.df1.b1'], 'contains': ['96.bb1.a1', '96.be1.a1', '96.bg1.a1', '144.bv1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1231, -1, 1605, -1, 600, -1, 1052, -1], 'generators': [3, 144, 576, 384], 'label': '1152.155799.48.cm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '48.cm1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60968340
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '48.cn1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1.a1', '24.df1.b1', '24.dg1.a1'], 'contains': ['96.bc1.a1', '96.bd1.a1', '96.bg1.a1', '144.bw1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [988, -1, 1690, -1, 272, -1, 1014, -1], 'generators': [97, 2, 576, 384], 'label': '1152.155799.48.cn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '48.cn1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cn1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60968341
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '48.cn1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1.a1', '24.df1.a1', '24.dg1.b1'], 'contains': ['96.bc1.b1', '96.bd1.a1', '96.bg1.a1', '144.bw1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [988, -1, 1381, -1, 272, -1, 1091, -1], 'generators': [145, 2, 576, 384], 'label': '1152.155799.48.cn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '48.cn1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cn1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60968342
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '48.co1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.v1.a1', '24.df1.b1', '24.dg1.a1'], 'contains': ['96.bc1.a1', '96.be1.a1', '96.bf1.a1', '144.bx1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [951, -1, 1464, -1, 312, -1, 880, -1], 'generators': [97, 98, 576, 384], 'label': '1152.155799.48.co1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '48.co1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.co1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60968343
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '48.co1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.v1.a1', '24.df1.a1', '24.dg1.b1'], 'contains': ['96.bc1.b1', '96.be1.a1', '96.bf1.a1', '144.bx1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [951, -1, 1348, -1, 312, -1, 917, -1], 'generators': [145, 98, 576, 384], 'label': '1152.155799.48.co1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '48.co1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.co1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60968344
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '48.cp1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '96.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '24.by1.a1', '24.dg1.a1', '24.dg1.b1'], 'contains': ['96.d1.a1', '96.bd1.a1', '96.bf1.a1', '144.by1.a1'], 'core': '96.d1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [438, -1, 660, -1, 222, -1, 535, -1], 'generators': [2, 96, 384, 576], 'label': '1152.155799.48.cp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '48.cp1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cp1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60968345
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '48.cq1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '24.bz1.a1', '24.de1.a1', '24.de1.b1'], 'contains': ['96.e1.a1', '144.by1.a1', '192.j1.a1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [39, -1, 159, -1, 135, -1, 131, -1], 'generators': [2, 32, 672, 576], 'label': '1152.155799.48.cq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '48.cq1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cq1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60968346
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '48.cr1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 192, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '24.ca1.a1', '24.dg1.a1', '24.dg1.b1'], 'contains': ['96.d1.a1', '96.be1.a1', '96.bg1.a1', '144.bz1.a1'], 'core': '96.d1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [483, -1, 702, -1, 171, -1, 487, -1], 'generators': [3, 96, 576, 384], 'label': '1152.155799.48.cr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '48.cr1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cr1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 60968347
    {'ambient': '1152.155799', 'aut_centralizer_order': 12, 'aut_label': '6.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 36, 'centralizer': '96.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.b1.a1'], 'contains': ['12.c1.a1', '12.be1.a1', '12.bf1.a1', '12.bm1.a1', '12.bn1.a1', '12.bv1.a1', '12.ca1.a1', '18.l1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5833, -1, 6762, -1, 6524, -1, 6613, -1], 'generators': [2, 576, 24, 12, 48, 96, 384], 'label': '1152.155799.6.p1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.p1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.p1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60968348
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '48.cs1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '24.cb1.a1', '24.de1.a1', '24.de1.b1'], 'contains': ['96.e1.a1', '144.bz1.a1', '192.l1.a1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [11, -1, 75, -1, 44, -1, 85, -1], 'generators': [3, 32, 672, 576], 'label': '1152.155799.48.cs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1.a1', 'old_label': '48.cs1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cs1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60968349
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '48.ct1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '24.cc1.a1'], 'contains': ['96.bh1.a1', '144.bz1.a1', '192.m1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [515, -1, 733, -1, 12, -1, 219, -1], 'generators': [3, 416, 672, 576], 'label': '1152.155799.48.ct1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cc1.a1', 'old_label': '48.ct1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ct1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60968350
    {'ambient': '1152.155799', 'aut_centralizer_order': 288, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '32.b1.a1', '32.c1.a1', '32.d1.a1', '32.e1.a1', '32.f1.a1', '32.g1.a1', '32.h1.a1'], 'contains': ['128.a1.a1', '192.a1.a1', '192.c1.a1', '192.d1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1133, -1, 1123, -1, 2668, -1, 1980, -1], 'generators': [48, 32, 384], 'label': '1152.155799.64.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '64.a1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968351
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '64.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '48.ca1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '32.b1.a1', '32.i1.a1'], 'contains': ['128.a1.a1', '192.b1.a1', '192.e1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [224, -1, 191, -1, 1312, -1, 600, -1], 'generators': [1, 32, 384], 'label': '1152.155799.64.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '64.b1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968352
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '64.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '48.ca1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b1', '32.b1.a1', '32.i1.b1'], 'contains': ['128.a1.a1', '192.b1.b1', '192.e1.b1'], 'core': '192.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [224, -1, 339, -1, 1312, -1, 416, -1], 'generators': [49, 32, 384], 'label': '1152.155799.64.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '64.b1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.b1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968353
    {'ambient': '1152.155799', 'aut_centralizer_order': 24, 'aut_label': '64.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '32.c1.a1', '32.i1.a1', '32.i1.b1'], 'contains': ['128.a1.a1', '192.i1.a1', '192.j1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [294, -1, 289, -1, 1253, -1, 543, -1], 'generators': [2, 384, 32], 'label': '1152.155799.64.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1.a1', 'old_label': '64.c1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968354
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '64.d1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '36.10', 'aut_weyl_index': 128, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '32.d1.a1', '32.i1.a1', '32.i1.b1'], 'contains': ['128.a1.a1', '192.k1.a1', '192.l1.a1', '192.m1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [133, -1, 247, -1, 1171, -1, 464, -1], 'generators': [3, 32, 384], 'label': '1152.155799.64.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1.a1', 'old_label': '64.d1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.d1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 60968355
    {'ambient': '1152.155799', 'aut_centralizer_order': 384, 'aut_label': '72.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.e1.a1', '24.ci1.a1', '36.a1.a1', '36.k1.a1', '36.bn1.a1', '36.bo1.a1', '36.bp1.a1', '36.bq1.a1', '36.br1.a1'], 'contains': ['144.a1.a1', '144.k1.a1', '144.l1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5150, 4993, 5490, 7341, 5387, 5537, 5454, 6835], 'generators': [24, 96, 576], 'label': '1152.155799.72.a1.a1', 'mobius_quo': 0, 'mobius_sub': -72, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['24.c1.a1', '24.e1.a1', '36.a1.a1'], 'normal_contains': ['144.a1.a1', '288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '576.8312', 'quotient_action_image': '6.1', 'quotient_action_kernel': '12.4', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968356
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '36.b1.a1', '36.c1.a1', '36.j1.a1'], 'contains': ['144.c1.a1', '144.d1.a1', '144.i1.a1', '144.j1.a1', '144.u1.a1', '144.bp1.a1', '144.bp1.b1', '144.bs1.a1', '144.bs1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3196, -1, 3329, -1, 1930, -1, 2776, -1], 'generators': [1, 2, 48, 576], 'label': '1152.155799.72.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.b1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968357
    {'ambient': '1152.155799', 'aut_centralizer_order': 128, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '36.c1.a1', '36.d1.a1', '36.e1.a1', '36.f1.a1', '36.g1.a1', '36.h1.a1', '36.k1.a1'], 'contains': ['144.c1.a1', '144.e1.a1', '144.f1.a1', '144.k1.a1', '144.m1.a1', '144.v1.a1', '144.w1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6901, -1, 6822, -1, 5629, -1, 6519, -1], 'generators': [1, 24, 96], 'label': '1152.155799.72.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.c1.a1', 'projective_image': '576.8312', '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': '2.1'}
  • id: 60968358
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '6.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.b1.a1'], 'contains': ['12.d1.a1', '12.bg1.a1', '12.bh1.a1', '12.bo1.a1', '12.bp1.a1', '12.bv1.a1', '12.cb1.a1', '18.m1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6103, -1, 6400, -1, 6125, -1, 6521, -1], 'generators': [13, 48, 576, 2, 384, 96, 24], 'label': '1152.155799.6.q1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.q1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.q1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968359
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '36.b1.a1', '36.i1.a1', '36.k1.a1'], 'contains': ['144.c1.a1', '144.f1.a1', '144.l1.a1', '144.n1.a1', '144.x1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4076, -1, 4275, -1, 3726, -1, 5216, -1], 'generators': [1, 600, 96], 'label': '1152.155799.72.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.d1.a1', 'projective_image': '576.8312', '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': '2.1'}
  • id: 60968360
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '36.b1.a1', '36.d1.a1', '36.j1.a1'], 'contains': ['144.c1.a1', '144.o1.a1', '144.s1.a1', '144.bq1.a1', '144.bq1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2579, -1, 3416, -1, 1877, -1, 2195, -1], 'generators': [1, 98, 48], 'label': '1152.155799.72.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.e1.a1', 'projective_image': '576.8312', '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': '4.2'}
  • id: 60968361
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '72.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '36.e1.a1', '36.i1.a1', '36.l1.a1'], 'contains': ['144.c1.a1', '144.g1.a1', '144.p1.a1', '144.t1.a1', '144.y1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5071, -1, 5284, -1, 4667, -1, 6065, -1], 'generators': [1, 6, 96], 'label': '1152.155799.72.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '72.f1.a1', 'projective_image': '576.8312', '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': '4.2'}
  • id: 60968362
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '36.f1.a1', '36.i1.a1', '36.l1.a1'], 'contains': ['144.c1.a1', '144.q1.a1', '144.r1.a1', '144.bt1.a1', '144.bt1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4551, -1, 4988, -1, 3657, -1, 5150, -1], 'generators': [1, 582, 96], 'label': '1152.155799.72.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '72.g1.a1', 'projective_image': '576.8312', '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': '4.2'}
  • id: 60968363
    {'ambient': '1152.155799', 'aut_centralizer_order': 128, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.f1.a1', '36.j1.a1', '36.k1.a1', '36.l1.a1'], 'contains': ['144.a1.a1', '144.c1.a1', '144.h1.a1', '144.bo1.a1', '144.bo1.b1', '144.br1.a1', '144.br1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1937, -1, 2266, -1, 1824, -1, 2078, -1], 'generators': [1, 48, 96, 576], 'label': '1152.155799.72.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.h1.a1', 'projective_image': '576.8312', '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': '6.1'}
  • id: 60968364
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.p1.a1', '36.c1.a1', '36.m1.a1', '36.n1.a1'], 'contains': ['144.d1.a1', '144.e1.a1', '144.z1.a1', '144.bb1.a1', '144.bd1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6773, -1, 7400, -1, 6357, -1, 6813, -1], 'generators': [1, 2, 24], 'label': '1152.155799.72.i1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.i1.a1', 'projective_image': '576.8312', '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': '8.3'}
  • id: 60968365
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '36.c1.a1'], 'contains': ['144.d1.a1', '144.f1.a1', '144.ba1.a1', '144.bc1.a1', '144.be1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7845, -1, 7824, -1, 5006, -1, 4414, -1], 'generators': [1, 2, 600], 'label': '1152.155799.72.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '72.j1.a1', 'projective_image': '576.8312', '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': '8.3'}
  • id: 60968366
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.r1.a1', '36.e1.a1', '36.m1.a1', '36.n1.a1'], 'contains': ['144.e1.a1', '144.g1.a1', '144.bf1.a1', '144.bg1.a1', '144.bm1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8561, -1, 8701, -1, 6946, -1, 7786, -1], 'generators': [1, 6, 24], 'label': '1152.155799.72.k1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.k1.a1', 'projective_image': '576.8312', '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': '8.3'}
  • id: 60968368
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '72.m1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.a1', '36.g1.a1', '36.h1.a1', '36.n1.a1'], 'contains': ['144.e1.a1', '144.bh1.a1', '144.bj1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8616, -1, 8622, -1, 7863, -1, 9426, -1], 'generators': [1, 108], 'label': '1152.155799.72.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.m1.a1', 'projective_image': '576.8312', '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': '2.1'}
  • id: 60968369
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1152.157863', 'aut_weyl_index': 4, 'centralizer': '144.b1.a1', 'complements': ['576.f1.a1', '576.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.f1.a1', '4.g1.a1', '6.a1.a1', '6.e1.a1', '8.f1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4506, 8486, 5712, 3501, 7036, 7651, 4329, 3478], 'generators': [1, 48, 672, 12, 24, 384, 576, 32], 'label': '1152.155799.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.f1.a1', '4.g1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '576.8312', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 60968370
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '6.r1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20051', 'aut_weyl_index': 12, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.cd1.a1', '12.ce1.a1', '18.m1.a1', '24.cw1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4095, -1, 4472, -1, 7397, -1, 3715, -1], 'generators': [13, 672, 32, 2, 576, 24, 48], 'label': '1152.155799.6.r1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.r1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.r1.a1', 'subgroup_fusion': None, 'weyl_group': '96.187'}
  • id: 60968371
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.a1', '36.e1.a1'], 'contains': ['144.f1.a1', '144.g1.a1', '144.bk1.a1', '144.bl1.a1', '144.bn1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9184, -1, 9071, -1, 5754, -1, 7402, -1], 'generators': [1, 6, 120], 'label': '1152.155799.72.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '72.n1.a1', 'projective_image': '576.8312', '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': '8.3'}
  • id: 60968372
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1.a1', '36.j1.a1', '36.o1.a1', '36.p1.a1'], 'contains': ['144.h1.a1', '144.i1.a1', '144.s1.a1', '144.bw1.a1', '144.bw1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2521, -1, 3211, -1, 1509, -1, 2422, -1], 'generators': [97, 2, 48], 'label': '1152.155799.72.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.o1.a1', 'projective_image': '576.8312', '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': '8.5'}
  • id: 60968373
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '72.p1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.v1.a1', '36.j1.a1', '36.o1.a1', '36.q1.a1'], 'contains': ['144.h1.a1', '144.j1.a1', '144.o1.a1', '144.bx1.a1', '144.bx1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2466, -1, 3146, -1, 1707, -1, 2257, -1], 'generators': [97, 98, 48], 'label': '1152.155799.72.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.p1.a1', 'projective_image': '576.8312', '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': '8.5'}
  • id: 60968374
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '72.q1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.w1.a1', '36.k1.a1', '36.p1.a1', '36.q1.a1', '36.r1.a1', '36.s1.a1', '36.t1.a1', '36.u1.a1'], 'contains': ['144.h1.a1', '144.k1.a1', '144.n1.a1', '144.v1.a1', '144.x1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6190, -1, 6426, -1, 6112, -1, 6384, -1], 'generators': [577, 24, 96], 'label': '1152.155799.72.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.q1.a1', 'projective_image': '576.8312', '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': '2.1'}
  • id: 60968375
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '72.r1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.x1.a1', '36.k1.a1', '36.o1.a1', '36.v1.a1'], 'contains': ['144.h1.a1', '144.l1.a1', '144.m1.a1', '144.w1.a1', '144.x1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3815, -1, 4202, -1, 3588, -1, 5282, -1], 'generators': [577, 600, 96], 'label': '1152.155799.72.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.r1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.r1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968376
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '72.s1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1.a1', '36.l1.a1', '36.r1.a1', '36.v1.a1'], 'contains': ['144.h1.a1', '144.p1.a1', '144.r1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4266, -1, 4523, -1, 4130, -1, 5625, -1], 'generators': [577, 6], 'label': '1152.155799.72.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '72.s1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.s1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60968377
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '72.t1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.z1.a1', '36.l1.a1', '36.s1.a1', '36.v1.a1'], 'contains': ['144.h1.a1', '144.q1.a1', '144.t1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4405, -1, 4565, -1, 4080, -1, 5712, -1], 'generators': [577, 582], 'label': '1152.155799.72.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '72.t1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.t1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60968378
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '72.u1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1.a1', '36.c1.a1', '36.o1.a1', '36.bm1.a1'], 'contains': ['144.i1.a1', '144.j1.a1', '144.m1.a1', '144.z1.a1', '144.ba1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2714, -1, 3583, -1, 2927, -1, 3695, -1], 'generators': [25, 2, 576], 'label': '1152.155799.72.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.u1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.u1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60968379
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '72.v1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bb1.a1', '36.b1.a1', '36.o1.a1', '36.bn1.a1'], 'contains': ['144.i1.a1', '144.l1.a1', '144.o1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3280, -1, 3785, -1, 2341, -1, 3312, -1], 'generators': [2, 120], 'label': '1152.155799.72.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '72.v1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.v1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60968380
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '72.w1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bc1.a1', '36.b1.a1', '36.p1.a1', '36.bm1.a1'], 'contains': ['144.i1.a1', '144.n1.a1', '144.s1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3340, -1, 3898, -1, 2192, -1, 3198, -1], 'generators': [121, 2], 'label': '1152.155799.72.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.w1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.w1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60968381
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '6.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '3.b1.a1'], 'contains': ['12.d1.a1', '12.bi1.a1', '12.bj1.a1', '12.bq1.a1', '12.br1.a1', '12.bx1.a1', '12.ca1.a1', '18.n1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6296, -1, 6901, -1, 6414, -1, 6719, -1], 'generators': [13, 48, 96, 6, 384, 576, 24], 'label': '1152.155799.6.s1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.s1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.s1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968382
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '72.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bd1.a1', '36.c1.a1', '36.p1.a1', '36.w1.a1', '36.x1.a1', '36.y1.a1', '36.z1.a1', '36.bn1.a1'], 'contains': ['144.i1.a1', '144.k1.a1', '144.bb1.a1', '144.bc1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7392, -1, 6877, -1, 6237, -1, 6322, -1], 'generators': [2, 24, 576], 'label': '1152.155799.72.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.x1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.x1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968383
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '72.y1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.be1.a1', '36.b1.a1', '36.o1.a1', '36.bo1.a1'], 'contains': ['144.j1.a1', '144.l1.a1', '144.s1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3020, -1, 3743, -1, 2291, -1, 3150, -1], 'generators': [3, 120], 'label': '1152.155799.72.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.y1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.y1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60968384
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '72.z1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bf1.a1', '36.b1.a1', '36.q1.a1', '36.bm1.a1'], 'contains': ['144.j1.a1', '144.n1.a1', '144.o1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3141, -1, 3537, -1, 2241, -1, 3102, -1], 'generators': [121, 98], 'label': '1152.155799.72.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.z1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.z1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60968385
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '72.ba1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bg1.a1', '36.c1.a1', '36.q1.a1', '36.ba1.a1', '36.bb1.a1', '36.bc1.a1', '36.bd1.a1', '36.bo1.a1'], 'contains': ['144.j1.a1', '144.k1.a1', '144.bd1.a1', '144.be1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6675, -1, 7602, -1, 6177, -1, 6263, -1], 'generators': [3, 24, 576], 'label': '1152.155799.72.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.ba1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968386
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '72.bb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bh1.a1', '36.d1.a1', '36.q1.a1', '36.be1.a1', '36.bf1.a1', '36.bg1.a1', '36.bh1.a1', '36.bn1.a1'], 'contains': ['144.k1.a1', '144.o1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5728, -1, 5985, -1, 6057, -1, 6176, -1], 'generators': [98, 24], 'label': '1152.155799.72.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.bb1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968387
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '72.bc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bi1.a1', '36.e1.a1', '36.r1.a1', '36.w1.a1', '36.ba1.a1', '36.be1.a1', '36.bi1.a1', '36.bp1.a1'], 'contains': ['144.k1.a1', '144.p1.a1', '144.bf1.a1', '144.bk1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8347, -1, 7466, -1, 6845, -1, 7570, -1], 'generators': [6, 24, 96], 'label': '1152.155799.72.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.bc1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968388
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '72.bd1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bj1.a1', '36.f1.a1', '36.s1.a1', '36.x1.a1', '36.bb1.a1', '36.bf1.a1', '36.bj1.a1', '36.bp1.a1'], 'contains': ['144.k1.a1', '144.q1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5878, -1, 6186, -1, 6734, -1, 6611, -1], 'generators': [582, 24], 'label': '1152.155799.72.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.bd1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968389
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '72.be1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bk1.a1', '36.f1.a1', '36.r1.a1', '36.y1.a1', '36.bc1.a1', '36.bg1.a1', '36.bk1.a1', '36.bq1.a1'], 'contains': ['144.k1.a1', '144.r1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6104, -1, 5919, -1, 6017, -1, 6572, -1], 'generators': [583, 24], 'label': '1152.155799.72.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.be1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.be1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968390
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '72.bf1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bl1.a1', '36.d1.a1', '36.p1.a1', '36.bi1.a1', '36.bj1.a1', '36.bk1.a1', '36.bl1.a1', '36.bo1.a1'], 'contains': ['144.k1.a1', '144.s1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6140, -1, 6095, -1, 5976, -1, 6215, -1], 'generators': [99, 24], 'label': '1152.155799.72.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.bf1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968391
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '72.bg1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bm1.a1', '36.e1.a1', '36.s1.a1', '36.z1.a1', '36.bd1.a1', '36.bh1.a1', '36.bl1.a1', '36.bq1.a1'], 'contains': ['144.k1.a1', '144.t1.a1', '144.bg1.a1', '144.bl1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7014, -1, 8321, -1, 6784, -1, 7496, -1], 'generators': [7, 24, 96], 'label': '1152.155799.72.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.bg1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 60968392
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '6.t1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '3.b1.a1'], 'contains': ['12.c1.a1', '12.bk1.a1', '12.bl1.a1', '12.bs1.a1', '12.bt1.a1', '12.bx1.a1', '12.cb1.a1', '18.o1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6008, -1, 6476, -1, 5761, -1, 6262, -1], 'generators': [3, 48, 576, 12, 384, 96, 24], 'label': '1152.155799.6.t1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.t1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.t1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968393
    {'ambient': '1152.155799', 'aut_centralizer_order': 384, 'aut_label': '72.bh1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bn1.a1', '36.a1.a1', '36.g1.a1', '36.t1.a1', '36.w1.a1', '36.bd1.a1', '36.bf1.a1', '36.bk1.a1'], 'contains': ['144.b1.a1', '144.k1.a1', '144.bh1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6521, -1, 6726, -1, 7803, -1, 7963, -1], 'generators': [12, 96], 'label': '1152.155799.72.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.bh1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968394
    {'ambient': '1152.155799', 'aut_centralizer_order': 192, 'aut_label': '72.bi1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bo1.a1', '36.a1.a1', '36.h1.a1', '36.u1.a1', '36.x1.a1', '36.bc1.a1', '36.be1.a1', '36.bl1.a1'], 'contains': ['144.k1.a1', '144.bh1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7570, -1, 7350, -1, 7434, -1, 7628, -1], 'generators': [588, 96], 'label': '1152.155799.72.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.bi1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968395
    {'ambient': '1152.155799', 'aut_centralizer_order': 128, 'aut_label': '72.bj1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bp1.a1', '36.g1.a1', '36.u1.a1', '36.z1.a1', '36.ba1.a1', '36.bg1.a1', '36.bj1.a1', '36.br1.a1'], 'contains': ['144.k1.a1', '144.bi1.a1', '144.bj1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6960, -1, 7263, -1, 7743, -1, 8598, -1], 'generators': [13, 96], 'label': '1152.155799.72.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.bj1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968396
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '72.bk1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bq1.a1', '36.h1.a1', '36.t1.a1', '36.y1.a1', '36.bb1.a1', '36.bh1.a1', '36.bi1.a1', '36.br1.a1'], 'contains': ['144.k1.a1', '144.bj1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6827, -1, 6954, -1, 7494, -1, 7686, -1], 'generators': [589, 96], 'label': '1152.155799.72.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.bk1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968397
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '72.bl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.br1.a1', '36.i1.a1', '36.v1.a1', '36.bp1.a1'], 'contains': ['144.l1.a1', '144.p1.a1', '144.q1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5007, -1, 5139, -1, 4337, -1, 6012, -1], 'generators': [6, 600], 'label': '1152.155799.72.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '72.bl1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60968398
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '72.bm1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bs1.a1', '36.i1.a1', '36.v1.a1', '36.bq1.a1'], 'contains': ['144.l1.a1', '144.r1.a1', '144.t1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4933, -1, 4928, -1, 4297, -1, 5904, -1], 'generators': [7, 600], 'label': '1152.155799.72.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '72.bm1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60968399
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '72.bn1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bt1.a1', '36.d1.a1', '36.o1.a1', '36.bm1.a1'], 'contains': ['144.m1.a1', '144.o1.a1', '144.s1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2406, -1, 3254, -1, 2146, -1, 2739, -1], 'generators': [25, 98], 'label': '1152.155799.72.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.bn1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60968400
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '72.bo1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bu1.a1', '36.e1.a1', '36.v1.a1', '36.bs1.a1'], 'contains': ['144.m1.a1', '144.p1.a1', '144.t1.a1', '144.bm1.a1', '144.bn1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4670, -1, 4612, -1, 5067, -1, 6127, -1], 'generators': [25, 6, 96], 'label': '1152.155799.72.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '72.bo1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60968401
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '72.bp1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bv1.a1', '36.f1.a1', '36.v1.a1', '36.bs1.a1'], 'contains': ['144.m1.a1', '144.q1.a1', '144.r1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4357, -1, 4696, -1, 4175, -1, 5668, -1], 'generators': [25, 582], 'label': '1152.155799.72.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '72.bp1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60968402
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '72.bq1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bw1.a1', '36.i1.a1', '36.r1.a1', '36.bs1.a1'], 'contains': ['144.n1.a1', '144.p1.a1', '144.r1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4970, -1, 5186, -1, 4256, -1, 5755, -1], 'generators': [601, 6], 'label': '1152.155799.72.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '72.bq1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60968403
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '6.u1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20051', 'aut_weyl_index': 12, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '3.a1.a1'], 'contains': ['12.e1.a1', '12.by1.a1', '12.ce1.a1', '18.n1.a1', '24.db1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4325, -1, 4921, -1, 7475, -1, 3999, -1], 'generators': [13, 96, 32, 6, 576, 24, 48], 'label': '1152.155799.6.u1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.u1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.u1.a1', 'subgroup_fusion': None, 'weyl_group': '96.187'}
  • id: 60968404
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '72.br1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bx1.a1', '36.i1.a1', '36.s1.a1', '36.bs1.a1'], 'contains': ['144.n1.a1', '144.q1.a1', '144.t1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4730, -1, 5035, -1, 4216, -1, 5794, -1], 'generators': [601, 582], 'label': '1152.155799.72.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '72.br1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.br1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60968405
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '72.bs1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.by1.a1', '24.bz1.a1', '36.j1.a1', '36.bm1.a1', '36.bn1.a1'], 'contains': ['144.a1.a1', '144.i1.a1', '144.o1.a1', '144.bu1.a1', '144.by1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1672, -1, 2075, -1, 1303, -1, 2032, -1], 'generators': [2, 48, 96], 'label': '1152.155799.72.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '72.bs1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60968406
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '72.bt1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ca1.a1', '24.cb1.a1', '24.cc1.a1', '36.j1.a1', '36.bm1.a1', '36.bo1.a1'], 'contains': ['144.a1.a1', '144.j1.a1', '144.s1.a1', '144.bv1.a1', '144.bz1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1742, -1, 2226, -1, 1140, -1, 1974, -1], 'generators': [3, 48, 96], 'label': '1152.155799.72.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.bt1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60968407
    {'ambient': '1152.155799', 'aut_centralizer_order': 128, 'aut_label': '72.bu1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.cf1.a1', '36.k1.a1', '36.bm1.a1', '36.bs1.a1'], 'contains': ['144.a1.a1', '144.m1.a1', '144.n1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2355, -1, 2720, -1, 2794, -1, 4649, -1], 'generators': [25, 96, 576], 'label': '1152.155799.72.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.bu1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968408
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '72.bv1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cd1.a1', '24.cg1.a1', '36.l1.a1', '36.bp1.a1', '36.bs1.a1'], 'contains': ['144.a1.a1', '144.p1.a1', '144.q1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2633, -1, 2931, -1, 4031, -1, 5397, -1], 'generators': [6, 576], 'label': '1152.155799.72.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '72.bv1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60968409
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '72.bw1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ce1.a1', '24.ch1.a1', '24.cj1.a1', '36.l1.a1', '36.bq1.a1', '36.bs1.a1'], 'contains': ['144.a1.a1', '144.r1.a1', '144.t1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2899, -1, 2804, -1, 3528, -1, 4953, -1], 'generators': [7, 576], 'label': '1152.155799.72.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '72.bw1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 60968410
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '72.bx1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ck1.a1', '36.c1.a1', '36.bt1.a1', '36.bu1.a1'], 'contains': ['144.u1.a1', '144.v1.a1', '144.ba1.a1', '144.bb1.a1', '144.bd1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8937, -1, 9367, -1, 6588, -1, 7188, -1], 'generators': [577, 2, 24], 'label': '1152.155799.72.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.bx1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60968411
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '72.by1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cl1.a1', '36.c1.a1'], 'contains': ['144.u1.a1', '144.w1.a1', '144.z1.a1', '144.bc1.a1', '144.be1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7776, -1, 7903, -1, 4946, -1, 4357, -1], 'generators': [577, 2, 600], 'label': '1152.155799.72.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '72.by1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.by1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60968412
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '72.bz1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cm1.a1', '36.e1.a1', '36.bt1.a1', '36.bu1.a1'], 'contains': ['144.v1.a1', '144.y1.a1', '144.bf1.a1', '144.bg1.a1', '144.bn1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9239, -1, 9505, -1, 7334, -1, 8656, -1], 'generators': [97, 6, 24], 'label': '1152.155799.72.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.bz1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60968413
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '72.ca1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cn1.a1', '36.g1.a1', '36.t1.a1', '36.bt1.a1'], 'contains': ['144.b1.a1', '144.v1.a1', '144.bj1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8044, -1, 7695, -1, 8455, -1, 9146, -1], 'generators': [97, 12], 'label': '1152.155799.72.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.ca1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968414
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '6.v1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20051', 'aut_weyl_index': 12, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '3.a1.a1'], 'contains': ['12.f1.a1', '12.by1.a1', '12.cd1.a1', '18.o1.a1', '24.dc1.a1'], 'core': '12.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3610, -1, 4579, -1, 7110, -1, 3641, -1], 'generators': [3, 672, 32, 12, 576, 24, 48], 'label': '1152.155799.6.v1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.v1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.v1.a1', 'subgroup_fusion': None, 'weyl_group': '96.187'}
  • id: 60968415
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '72.cb1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.co1.a1', '36.g1.a1', '36.u1.a1', '36.bu1.a1'], 'contains': ['144.v1.a1', '144.bh1.a1', '144.bi1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7960, -1, 8571, -1, 8664, -1, 9369, -1], 'generators': [97, 108], 'label': '1152.155799.72.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.cb1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968416
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '72.cc1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 576, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cp1.a1', '36.h1.a1', '36.t1.a1', '36.u1.a1'], 'contains': ['144.v1.a1', '144.bh1.a1', '144.bj1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7500, -1, 7745, -1, 7683, -1, 9012, -1], 'generators': [577, 108], 'label': '1152.155799.72.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1.a1', 'old_label': '72.cc1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60968417
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '72.cd1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cq1.a1', '36.e1.a1'], 'contains': ['144.w1.a1', '144.y1.a1', '144.bk1.a1', '144.bl1.a1', '144.bm1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9129, -1, 9020, -1, 5694, -1, 7344, -1], 'generators': [97, 6, 120], 'label': '1152.155799.72.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '72.cd1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60968418
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '72.ce1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cr1.a1', '24.cv1.a1', '36.m1.a1', '36.w1.a1', '36.bt1.a1'], 'contains': ['144.b1.a1', '144.bb1.a1', '144.bf1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8285, -1, 7307, -1, 8964, -1, 8231, -1], 'generators': [2, 12], 'label': '1152.155799.72.ce1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '72.ce1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60968419
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '72.cf1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cs1.a1', '36.n1.a1', '36.w1.a1', '36.bu1.a1'], 'contains': ['144.bb1.a1', '144.bf1.a1', '144.bh1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9286, -1, 9295, -1, 8507, -1, 9236, -1], 'generators': [2, 588], 'label': '1152.155799.72.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '72.cf1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60968420
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '72.cg1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ct1.a1', '24.cw1.a1', '36.m1.a1', '36.z1.a1', '36.bu1.a1'], 'contains': ['144.bb1.a1', '144.bg1.a1', '144.bi1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7439, -1, 8365, -1, 8878, -1, 8468, -1], 'generators': [13, 2], 'label': '1152.155799.72.cg1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.cg1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60968421
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '72.ch1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cu1.a1', '36.n1.a1', '36.z1.a1', '36.bt1.a1'], 'contains': ['144.bb1.a1', '144.bg1.a1', '144.bj1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8874, -1, 9461, -1, 8060, -1, 9278, -1], 'generators': [589, 2], 'label': '1152.155799.72.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.ch1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60968422
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '72.ci1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cx1.a1', '24.db1.a1', '36.m1.a1', '36.ba1.a1', '36.bu1.a1'], 'contains': ['144.bd1.a1', '144.bf1.a1', '144.bi1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8485, -1, 8430, -1, 8921, -1, 8510, -1], 'generators': [13, 6], 'label': '1152.155799.72.ci1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.ci1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60968423
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '72.cj1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cy1.a1', '36.n1.a1', '36.ba1.a1', '36.bt1.a1'], 'contains': ['144.bd1.a1', '144.bf1.a1', '144.bj1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9044, -1, 9425, -1, 8228, -1, 9319, -1], 'generators': [109, 6], 'label': '1152.155799.72.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.cj1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60968424
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '72.ck1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cz1.a1', '24.dc1.a1', '24.dd1.a1', '36.m1.a1', '36.bd1.a1', '36.bt1.a1'], 'contains': ['144.b1.a1', '144.bd1.a1', '144.bg1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6429, -1, 8179, -1, 8754, -1, 7836, -1], 'generators': [3, 12], 'label': '1152.155799.72.ck1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.ck1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60968425
    {'ambient': '1152.155799', 'aut_centralizer_order': 2, 'aut_label': '6.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '384.20051', 'aut_weyl_index': 12, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1'], 'contains': ['12.bz1.a1', '12.cg1.a1', '12.ch1.a1', '18.o1.a1', '24.dd1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4794, -1, 5389, -1, 5650, -1, 4168, -1], 'generators': [3, 672, 416, 12, 576, 24, 48], 'label': '1152.155799.6.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1.a1', 'old_label': '6.w1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.w1.a1', 'subgroup_fusion': None, 'weyl_group': '96.187'}
  • id: 60968426
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '72.cl1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.da1.a1', '36.n1.a1', '36.bd1.a1', '36.bu1.a1'], 'contains': ['144.bd1.a1', '144.bg1.a1', '144.bh1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9083, -1, 9259, -1, 8103, -1, 9195, -1], 'generators': [3, 588], 'label': '1152.155799.72.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.cl1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60968427
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '72.cm1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.df1.a1', '36.j1.a1'], 'contains': ['144.bo1.a1', '144.bp1.a1', '144.bq1.a1', '144.bu1.a1', '144.bv1.a1', '144.bw1.b1', '144.bx1.b1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1345, -1, 1536, -1, 711, -1, 965, -1], 'generators': [1, 2, 144], 'label': '1152.155799.72.cm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1.a1', 'old_label': '72.cm1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968428
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '72.cm1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.df1.b1', '36.j1.a1'], 'contains': ['144.bo1.b1', '144.bp1.b1', '144.bq1.b1', '144.bu1.a1', '144.bv1.a1', '144.bw1.a1', '144.bx1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1345, -1, 1742, -1, 711, -1, 832, -1], 'generators': [97, 2, 144], 'label': '1152.155799.72.cm1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1.a1', 'old_label': '72.cm1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cm1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968429
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '72.cn1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.de1.a1', '24.dg1.a1', '36.j1.a1'], 'contains': ['144.bp1.a1', '144.bq1.a1', '144.br1.a1', '144.bw1.a1', '144.bx1.a1', '144.by1.a1', '144.bz1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [383, -1, 546, -1, 362, -1, 593, -1], 'generators': [1, 2, 96], 'label': '1152.155799.72.cn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1.a1', 'old_label': '72.cn1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cn1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968430
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '72.cn1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.de1.b1', '24.dg1.b1', '36.j1.a1'], 'contains': ['144.bp1.b1', '144.bq1.b1', '144.br1.b1', '144.bw1.b1', '144.bx1.b1', '144.by1.a1', '144.bz1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [383, -1, 808, -1, 362, -1, 438, -1], 'generators': [49, 2, 96], 'label': '1152.155799.72.cn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1.a1', 'old_label': '72.cn1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cn1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968431
    {'ambient': '1152.155799', 'aut_centralizer_order': 384, 'aut_label': '96.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.a1.a1', '48.j1.a1', '48.k1.a1', '48.l1.a1', '48.m1.a1'], 'contains': ['192.a1.a1', '192.b1.a1', '192.b1.b1', '288.c1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7043, 3601, 7639, 2251, 3474, 4714, 3687, 1829], 'generators': [1, 48, 384], 'label': '1152.155799.96.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['24.a1.a1', '48.a1.a1'], 'normal_contains': ['192.a1.a1', '192.b1.b1', '192.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968432
    {'ambient': '1152.155799', 'aut_centralizer_order': 1152, 'aut_label': '96.b1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '48.a1.a1', '48.d1.a1', '48.e1.a1', '48.q1.a1', '48.bc1.a1', '48.bi1.a1', '48.bm1.a1', '48.bq1.a1', '48.br1.a1', '48.bs1.a1', '48.bt1.a1'], 'contains': ['192.a1.a1', '288.a1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8567, 6538, 8683, 5900, 6533, 6700, 7133, 4783], 'generators': [24, 384, 48], 'label': '1152.155799.96.b1.a1', 'mobius_quo': 0, 'mobius_sub': -96, 'normal_closure': '96.b1.a1', 'normal_contained_in': ['24.c1.a1', '48.a1.a1', '48.d1.a1', '48.e1.a1'], 'normal_contains': ['192.a1.a1', '288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.b1.a1', 'projective_image': '576.8312', 'quotient_action_image': '4.2', 'quotient_action_kernel': '24.13', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '96.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968433
    {'ambient': '1152.155799', 'aut_centralizer_order': 384, 'aut_label': '96.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '12.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '48.a1.a1', '48.s1.a1', '48.bd1.a1', '48.bg1.a1', '48.bw1.a1'], 'contains': ['192.a1.a1', '288.i1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7011, 5672, 7943, 3977, 3792, 5241, 5142, 3717], 'generators': [25, 48, 384], 'label': '1152.155799.96.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '96.c1.a1', 'normal_contained_in': ['24.d1.a1', '48.a1.a1'], 'normal_contains': ['192.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.c1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968434
    {'ambient': '1152.155799', 'aut_centralizer_order': 384, 'aut_label': '96.d1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '12.c1.a1', 'complements': ['12.j1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.b1.a1', '48.f1.a1', '48.f1.b1', '48.cp1.a1', '48.cr1.a1'], 'contains': ['192.f1.a1', '288.b1.a1'], 'core': '96.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [506, 1604, 644, 1212, 484, 3030, 769, 2582], 'generators': [96, 576, 384], 'label': '1152.155799.96.d1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '96.d1.a1', 'normal_contained_in': ['32.a1.a1', '48.b1.a1', '48.f1.b1', '48.f1.a1'], 'normal_contains': ['288.b1.a1', '384.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.d1.a1', 'projective_image': '1152.155799', 'quotient_action_image': '12.4', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '96.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968435
    {'ambient': '1152.155799', 'aut_centralizer_order': 192, 'aut_label': '96.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '24.b1.a1', 'complements': ['12.u1.a1', '12.ci1.a1', '12.v1.a1', '12.cj1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.c1.a1', '48.cf1.a1', '48.cf1.b1', '48.cq1.a1', '48.cs1.a1'], 'contains': ['288.b1.a1', '384.b1.a1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [16, 883, 52, 2697, 422, 2362, 201, 4162], 'generators': [32, 96, 576], 'label': '1152.155799.96.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '96.e1.a1', 'normal_contained_in': ['32.a1.a1', '48.c1.a1'], 'normal_contains': ['288.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.e1.a1', 'projective_image': '1152.155799', 'quotient_action_image': '2.1', 'quotient_action_kernel': '48.4', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '96.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60968436
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 16, 'centralizer': '144.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.a1', '4.i1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.b1.b1', '24.a1.a1', '24.f1.a1', '32.b1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1100, 662, 1001, 1849, 1473, 1102, 1426, 1368], 'generators': [1, 384, 576, 48, 32, 672], 'label': '1152.155799.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '16.b1.b1', '16.b1.a1', '24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '576.8312', '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': '144.183'}
  • id: 60968437
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '96.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '24.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '32.b1.a1', '48.g1.a1', '48.h1.a1', '48.i1.a1'], 'contains': ['192.c1.a1', '192.e1.a1', '192.e1.b1', '288.c1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [802, -1, 1014, -1, 2727, -1, 1841, -1], 'generators': [1, 48, 32], 'label': '1152.155799.96.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '96.f1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968438
    {'ambient': '1152.155799', 'aut_centralizer_order': 768, 'aut_label': '96.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '6.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '48.j1.a1', '48.n1.a1', '48.o1.a1', '48.p1.a1', '48.q1.a1', '48.r1.a1', '48.s1.a1', '48.t1.a1', '48.u1.a1', '48.v1.a1', '48.w1.a1', '48.x1.a1', '48.y1.a1', '48.z1.a1'], 'contains': ['192.a1.a1', '192.f1.a1', '192.g1.a1', '288.d1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3979, -1, 4151, -1, 2456, -1, 4018, -1], 'generators': [48, 96, 384], 'label': '1152.155799.96.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '96.g1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968439
    {'ambient': '1152.155799', 'aut_centralizer_order': 128, 'aut_label': '96.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '18.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '48.n1.a1', '48.bb1.a1', '48.bc1.a1', '48.bd1.a1', '48.be1.a1', '48.bf1.a1'], 'contains': ['192.a1.a1', '192.h1.a1', '192.h1.b1', '288.e1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7621, -1, 7842, -1, 3506, -1, 4063, -1], 'generators': [97, 48, 384], 'label': '1152.155799.96.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '96.h1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968440
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '96.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '48.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '48.k1.a1', '48.o1.a1', '48.bb1.a1', '48.bg1.a1', '48.bh1.a1', '48.bi1.a1', '48.bj1.a1'], 'contains': ['192.a1.a1', '192.i1.a1', '288.f1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6966, -1, 7011, -1, 3428, -1, 3299, -1], 'generators': [2, 48, 384], 'label': '1152.155799.96.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1.a1', 'old_label': '96.i1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968441
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '96.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bz1.a1', '32.c1.a1', '48.g1.a1', '48.bk1.a1', '48.bl1.a1'], 'contains': ['192.c1.a1', '192.j1.a1', '288.f1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [637, -1, 876, -1, 2622, -1, 1886, -1], 'generators': [2, 48, 32], 'label': '1152.155799.96.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.d1.a1', 'old_label': '96.j1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968442
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '96.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '48.k1.a1', '48.p1.a1', '48.bb1.a1', '48.bg1.a1', '48.bh1.a1', '48.bm1.a1', '48.bn1.a1'], 'contains': ['192.a1.a1', '192.k1.a1', '288.g1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6753, -1, 7050, -1, 3383, -1, 3255, -1], 'generators': [3, 48, 384], 'label': '1152.155799.96.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1.a1', 'old_label': '96.k1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.k1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968443
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '96.l1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cb1.a1', '32.d1.a1', '48.g1.a1', '48.bk1.a1', '48.bo1.a1'], 'contains': ['192.c1.a1', '192.l1.a1', '288.g1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [678, -1, 976, -1, 2590, -1, 1935, -1], 'generators': [3, 48, 32], 'label': '1152.155799.96.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.g1.a1', 'old_label': '96.l1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.l1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968444
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '96.m1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cc1.a1', '32.d1.a1', '48.bp1.a1'], 'contains': ['192.d1.a1', '192.m1.a1', '288.g1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [2055, -1, 2625, -1, 2407, -1, 2024, -1], 'generators': [3, 48, 416], 'label': '1152.155799.96.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bp1.a1', 'old_label': '96.m1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.m1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968445
    {'ambient': '1152.155799', 'aut_centralizer_order': 384, 'aut_label': '96.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.l1.a1', '48.q1.a1', '48.r1.a1', '48.bd1.a1', '48.be1.a1', '48.bj1.a1', '48.bn1.a1', '48.bu1.a1', '48.bv1.a1'], 'contains': ['192.a1.a1', '288.h1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8184, -1, 8246, -1, 4769, -1, 5341, -1], 'generators': [120, 384, 48], 'label': '1152.155799.96.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '96.n1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968446
    {'ambient': '1152.155799', 'aut_centralizer_order': 128, 'aut_label': '96.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.l1.a1', '48.s1.a1', '48.t1.a1', '48.bc1.a1', '48.be1.a1', '48.bh1.a1', '48.bx1.a1'], 'contains': ['192.a1.a1', '288.j1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7892, -1, 7510, -1, 3832, -1, 5180, -1], 'generators': [121, 48, 384], 'label': '1152.155799.96.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '96.o1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.o1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968447
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '8.b1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '48.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.a1.a1', '24.c1.a1', '24.e1.a1', '24.ci1.a1', '32.e1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3876, 3462, 5017, 6308, 4104, 3364, 3509, 5663], 'generators': [24, 576, 672, 32, 384, 48], 'label': '1152.155799.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'normal_contains': ['16.a1.a1', '24.c1.a1', '24.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 60968448
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '96.p1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '48.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1.a1', '48.m1.a1', '48.v1.a1', '48.bf1.a1', '48.bq1.a1', '48.bu1.a1', '48.bw1.a1', '48.bx1.a1'], 'contains': ['192.a1.a1', '288.k1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9726, -1, 8716, -1, 5086, -1, 6675, -1], 'generators': [6, 384, 48], 'label': '1152.155799.96.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '96.p1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.p1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968449
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '96.q1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '144.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.h1.a1', '48.m1.a1', '48.z1.a1', '48.bf1.a1', '48.br1.a1', '48.bv1.a1', '48.bw1.a1', '48.bx1.a1'], 'contains': ['192.a1.a1', '288.l1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8935, -1, 8919, -1, 5046, -1, 6637, -1], 'generators': [7, 48, 384], 'label': '1152.155799.96.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '96.q1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.q1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968450
    {'ambient': '1152.155799', 'aut_centralizer_order': 288, 'aut_label': '96.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '32.e1.a1', '48.h1.a1', '48.bl1.a1', '48.bo1.a1', '48.by1.a1', '48.bz1.a1', '48.ca1.a1', '48.cb1.a1'], 'contains': ['192.c1.a1', '288.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3738, -1, 4390, -1, 6698, -1, 3618, -1], 'generators': [24, 32, 48], 'label': '1152.155799.96.r1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '96.r1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.r1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968451
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '96.s1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '24.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cf1.a1', '32.f1.a1', '48.h1.a1', '48.bk1.a1', '48.cc1.a1'], 'contains': ['192.c1.a1', '288.i1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1632, -1, 2120, -1, 3661, -1, 3043, -1], 'generators': [25, 32, 48], 'label': '1152.155799.96.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '96.s1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.s1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968452
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '96.t1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cg1.a1', '32.g1.a1', '48.i1.a1', '48.by1.a1', '48.cc1.a1'], 'contains': ['192.c1.a1', '288.k1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1977, -1, 2363, -1, 4729, -1, 3759, -1], 'generators': [6, 48, 32], 'label': '1152.155799.96.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1.a1', 'old_label': '96.t1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.t1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968453
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '96.u1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ch1.a1', '32.h1.a1', '48.i1.a1', '48.bz1.a1', '48.cc1.a1'], 'contains': ['192.c1.a1', '288.l1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1851, -1, 2396, -1, 4689, -1, 3579, -1], 'generators': [7, 48, 32], 'label': '1152.155799.96.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.h1.a1', 'old_label': '96.u1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.u1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968454
    {'ambient': '1152.155799', 'aut_centralizer_order': 144, 'aut_label': '96.v1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ci1.a1', '32.e1.a1', '48.bp1.a1', '48.cd1.a1', '48.ce1.a1'], 'contains': ['192.d1.a1', '288.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4216, -1, 5407, -1, 5659, -1, 3971, -1], 'generators': [24, 416, 48], 'label': '1152.155799.96.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.n1.a1', 'old_label': '96.v1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.v1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968455
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '96.w1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cj1.a1', '32.h1.a1', '48.cd1.a1'], 'contains': ['192.d1.a1', '288.l1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3412, -1, 2735, -1, 4287, -1, 3928, -1], 'generators': [7, 48, 416], 'label': '1152.155799.96.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.cd1.a1', 'old_label': '96.w1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.w1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968456
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '96.x1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.de1.a1', '32.i1.a1', '48.g1.a1'], 'contains': ['192.e1.a1', '192.j1.a1', '192.l1.a1', '288.o1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [220, -1, 139, -1, 1207, -1, 499, -1], 'generators': [1, 2, 32], 'label': '1152.155799.96.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.g1.a1', 'old_label': '96.x1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.x1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968457
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '96.x1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.de1.b1', '32.i1.b1', '48.g1.a1'], 'contains': ['192.e1.b1', '192.j1.a1', '192.l1.a1', '288.o1.b1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [220, -1, 366, -1, 1207, -1, 356, -1], 'generators': [49, 2, 32], 'label': '1152.155799.96.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.g1.a1', 'old_label': '96.x1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.x1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968458
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 16, 'centralizer': '144.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.k1.a1', '4.l1.a1'], 'contains': ['16.a1.a1', '24.d1.a1', '24.cf1.a1', '32.f1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1363, 1965, 1993, 3012, 2481, 2310, 2319, 2365], 'generators': [25, 384, 576, 32, 48, 672], 'label': '1152.155799.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '24.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 60968459
    {'ambient': '1152.155799', 'aut_centralizer_order': 128, 'aut_label': '96.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '18.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.j1.a1', '48.cg1.a1', '48.ch1.a1', '48.ci1.a1'], 'contains': ['192.b1.a1', '192.f1.a1', '192.h1.a1', '288.m1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1501, -1, 1285, -1, 972, -1, 1500, -1], 'generators': [1, 96, 384], 'label': '1152.155799.96.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '96.y1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.y1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968460
    {'ambient': '1152.155799', 'aut_centralizer_order': 128, 'aut_label': '96.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '18.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.b1', '48.j1.a1', '48.cg1.b1', '48.ch1.b1', '48.ci1.b1'], 'contains': ['192.b1.b1', '192.f1.a1', '192.h1.b1', '288.m1.b1'], 'core': '192.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [1501, -1, 1901, -1, 972, -1, 1409, -1], 'generators': [49, 96, 384], 'label': '1152.155799.96.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '96.y1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.y1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968461
    {'ambient': '1152.155799', 'aut_centralizer_order': 128, 'aut_label': '96.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '18.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '48.cg1.a1', '48.cj1.a1', '48.ck1.a1'], 'contains': ['192.b1.a1', '192.g1.a1', '192.h1.b1', '288.n1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3769, -1, 3704, -1, 1538, -1, 2621, -1], 'generators': [1, 144, 384], 'label': '1152.155799.96.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '96.z1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.z1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968462
    {'ambient': '1152.155799', 'aut_centralizer_order': 128, 'aut_label': '96.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '18.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '48.cg1.b1', '48.cj1.b1', '48.ck1.b1'], 'contains': ['192.b1.b1', '192.g1.a1', '192.h1.a1', '288.n1.b1'], 'core': '192.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [3769, -1, 3755, -1, 1538, -1, 2652, -1], 'generators': [97, 144, 384], 'label': '1152.155799.96.z1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '96.z1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.z1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968463
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '96.ba1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.a1', '48.k1.a1', '48.ch1.a1', '48.cj1.a1'], 'contains': ['192.b1.a1', '192.i1.a1', '192.k1.a1', '288.o1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1914, -1, 2020, -1, 1358, -1, 1662, -1], 'generators': [1, 2, 384], 'label': '1152.155799.96.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.j1.a1', 'old_label': '96.ba1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968464
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '96.ba1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.b1', '48.k1.a1', '48.ch1.b1', '48.cj1.b1'], 'contains': ['192.b1.b1', '192.i1.a1', '192.k1.a1', '288.o1.b1'], 'core': '192.b1.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [1914, -1, 2234, -1, 1358, -1, 1470, -1], 'generators': [49, 2, 384], 'label': '1152.155799.96.ba1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.j1.a1', 'old_label': '96.ba1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ba1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968465
    {'ambient': '1152.155799', 'aut_centralizer_order': 384, 'aut_label': '96.bb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '12.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '48.cg1.a1', '48.cg1.b1', '48.cl1.a1', '48.cm1.a1'], 'contains': ['192.f1.a1', '192.g1.a1', '288.p1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1573, -1, 1940, -1, 1017, -1, 1613, -1], 'generators': [624, 96, 384], 'label': '1152.155799.96.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '96.bb1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968466
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '96.bc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.n1.a1', '48.cg1.b1', '48.cn1.a1', '48.co1.a1'], 'contains': ['192.f1.a1', '192.h1.a1', '288.q1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1168, -1, 1860, -1, 796, -1, 1439, -1], 'generators': [577, 96, 384], 'label': '1152.155799.96.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '96.bc1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968467
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '96.bc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.b1', '48.n1.a1', '48.cg1.a1', '48.cn1.b1', '48.co1.b1'], 'contains': ['192.f1.a1', '192.h1.b1', '288.q1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1168, -1, 1204, -1, 796, -1, 1378, -1], 'generators': [625, 96, 384], 'label': '1152.155799.96.bc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '96.bc1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bc1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968468
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '96.bd1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '48.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.a1', '48.ch1.a1', '48.ch1.b1', '48.cl1.a1', '48.cn1.a1', '48.cn1.b1', '48.cp1.a1'], 'contains': ['192.f1.a1', '192.i1.a1', '288.r1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1210, -1, 1668, -1, 718, -1, 1334, -1], 'generators': [2, 576, 384], 'label': '1152.155799.96.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '96.bd1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968469
    {'ambient': '1152.155799', 'aut_centralizer_order': 2, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '576.8553', 'aut_weyl_index': 8, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.j1.a1'], 'contains': ['16.c1.a1', '16.d1.a1', '16.f1.a1', '16.g1.a1', '16.h1.a1', '24.g1.a1', '24.p1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2411, -1, 3646, -1, 4893, -1, 2903, -1], 'generators': [1, 384, 32, 2, 24, 48], 'label': '1152.155799.8.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '8.d1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '144.144'}
  • id: 60968470
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '96.be1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1.a1', '48.ch1.a1', '48.ch1.b1', '48.cm1.a1', '48.co1.a1', '48.co1.b1', '48.cr1.a1'], 'contains': ['192.f1.a1', '192.k1.a1', '288.s1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1139, -1, 1522, -1, 672, -1, 1256, -1], 'generators': [3, 576, 384], 'label': '1152.155799.96.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '96.be1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.be1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968471
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '96.bf1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '48.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.u1.a1', '48.ci1.a1', '48.ci1.b1', '48.cl1.a1', '48.co1.a1', '48.co1.b1', '48.cp1.a1'], 'contains': ['192.f1.a1', '288.t1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [932, -1, 1356, -1, 606, -1, 874, -1], 'generators': [98, 384, 576], 'label': '1152.155799.96.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '96.bf1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968472
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '96.bg1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '144.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.y1.a1', '48.ci1.a1', '48.ci1.b1', '48.cm1.a1', '48.cn1.a1', '48.cn1.b1', '48.cr1.a1'], 'contains': ['192.f1.a1', '288.u1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1008, -1, 1389, -1, 566, -1, 1060, -1], 'generators': [99, 576, 384], 'label': '1152.155799.96.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '96.bg1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968473
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '96.bh1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.12', 'aut_weyl_index': 192, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.ba1.a1', '48.ct1.a1'], 'contains': ['288.b1.a1', '384.c1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [578, -1, 771, -1, 325, -1, 326, -1], 'generators': [416, 96, 576], 'label': '1152.155799.96.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '96.bh1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60968474
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '96.bi1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.n1.a1', '48.cg1.a1', '48.cg1.b1'], 'contains': ['192.g1.a1', '192.h1.a1', '192.h1.b1', '288.v1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2159, -1, 2048, -1, 1506, -1, 1797, -1], 'generators': [577, 144, 384], 'label': '1152.155799.96.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '96.bi1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968475
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '96.bj1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '48.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.a1', '48.cj1.a1', '48.cj1.b1'], 'contains': ['192.g1.a1', '192.i1.a1', '288.w1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3033, -1, 3372, -1, 1620, -1, 2577, -1], 'generators': [2, 624, 384], 'label': '1152.155799.96.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.k1.a1', 'old_label': '96.bj1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968476
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '96.bk1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1.a1', '48.cj1.a1', '48.cj1.b1'], 'contains': ['192.g1.a1', '192.k1.a1', '288.x1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2700, -1, 3276, -1, 1475, -1, 2533, -1], 'generators': [3, 624, 384], 'label': '1152.155799.96.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.k1.a1', 'old_label': '96.bk1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968477
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '96.bl1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '48.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.w1.a1', '48.ck1.a1', '48.ck1.b1'], 'contains': ['192.g1.a1', '288.y1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4423, -1, 4669, -1, 2817, -1, 4582, -1], 'generators': [582, 384, 144], 'label': '1152.155799.96.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.r1.a1', 'old_label': '96.bl1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968478
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '96.bm1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 384, 'centralizer': '144.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.x1.a1', '48.ck1.a1', '48.ck1.b1'], 'contains': ['192.g1.a1', '288.z1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4372, -1, 4466, -1, 2778, -1, 4487, -1], 'generators': [583, 144, 384], 'label': '1152.155799.96.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.r1.a1', 'old_label': '96.bm1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968479
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '96.bn1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bb1.a1', '48.ch1.a1', '48.cj1.b1'], 'contains': ['192.h1.a1', '192.i1.a1', '192.k1.a1', '288.ba1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2828, -1, 2676, -1, 1421, -1, 1765, -1], 'generators': [577, 2, 384], 'label': '1152.155799.96.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.j1.a1', 'old_label': '96.bn1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968480
    {'ambient': '1152.155799', 'aut_centralizer_order': 6, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '768.1090146', 'aut_weyl_index': 6, 'centralizer': '192.a1.a1', 'complements': ['576.b1.a1', '576.e1.a1', '576.b1.b1', '576.e1.b1', '576.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.d1.a1', '4.f1.a1', '6.b1.a1', '6.p1.a1', '8.k1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3461, 6891, 5566, 9574, 6524, 6173, 3924, 8691], 'generators': [2, 48, 32, 12, 24, 576, 672, 384], 'label': '1152.155799.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.d1.a1', '4.f1.a1', '6.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '576.8312', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': '192.1470'}
  • id: 60968481
    {'ambient': '1152.155799', 'aut_centralizer_order': 2, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '576.8553', 'aut_weyl_index': 8, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '4.j1.a1'], 'contains': ['16.d1.a1', '16.e1.a1', '16.i1.a1', '16.j1.a1', '16.m1.a1', '24.h1.a1', '24.r1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3010, -1, 4135, -1, 5510, -1, 3423, -1], 'generators': [1, 384, 32, 6, 24, 48], 'label': '1152.155799.8.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '8.e1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '144.144'}
  • id: 60968482
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '96.bn1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bb1.a1', '48.ch1.b1', '48.cj1.a1'], 'contains': ['192.h1.b1', '192.i1.a1', '192.k1.a1', '288.ba1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2828, -1, 2597, -1, 1421, -1, 1730, -1], 'generators': [625, 2, 384], 'label': '1152.155799.96.bn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.j1.a1', 'old_label': '96.bn1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bn1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968483
    {'ambient': '1152.155799', 'aut_centralizer_order': 288, 'aut_label': '128.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '64.a1.a1', '64.b1.a1', '64.b1.b1', '64.c1.a1', '64.d1.a1'], 'contains': ['384.a1.a1', '384.b1.a1', '384.c1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [116, -1, 278, -1, 1224, -1, 563, -1], 'generators': [32, 384], 'label': '1152.155799.128.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '128.a1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968484
    {'ambient': '1152.155799', 'aut_centralizer_order': 768, 'aut_label': '144.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '48.c1.a1', '48.ba1.a1', '72.a1.a1', '72.h1.a1', '72.bs1.a1', '72.bt1.a1', '72.bu1.a1', '72.bv1.a1', '72.bw1.a1'], 'contains': ['288.b1.a1', '288.d1.a1', '288.p1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1951, 2956, 2387, 3877, 1824, 3975, 2078, 5233], 'generators': [48, 96, 576], 'label': '1152.155799.144.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': ['48.b1.a1', '48.c1.a1', '72.a1.a1'], 'normal_contains': ['288.b1.a1', '576.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.a1.a1', 'projective_image': '576.8312', 'quotient_action_image': '6.1', 'quotient_action_kernel': '24.5', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968485
    {'ambient': '1152.155799', 'aut_centralizer_order': 1152, 'aut_label': '144.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '2.c1.a1', 'complements': ['8.o1.a1', '8.o1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '48.ca1.a1', '48.ce1.a1', '72.l1.a1', '72.bh1.a1', '72.ca1.a1', '72.ce1.a1', '72.ck1.a1'], 'contains': ['288.a1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6420, 7536, 6817, 6624, 8713, 7445, 7218, 6182], 'generators': [12], 'label': '1152.155799.144.b1.a1', 'mobius_quo': 0, 'mobius_sub': -72, 'normal_closure': '144.b1.a1', 'normal_contained_in': ['36.a1.a1', '48.d1.a1'], 'normal_contains': ['288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.b1.a1', 'projective_image': '576.8312', 'quotient_action_image': '2.1', 'quotient_action_kernel': '72.44', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '144.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968486
    {'ambient': '1152.155799', 'aut_centralizer_order': 256, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '72.b1.a1', '72.c1.a1', '72.d1.a1', '72.e1.a1', '72.f1.a1', '72.g1.a1', '72.h1.a1'], 'contains': ['288.c1.a1', '288.d1.a1', '288.e1.a1', '288.m1.a1', '288.m1.b1', '288.n1.a1', '288.n1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3976, -1, 4157, -1, 2556, -1, 3653, -1], 'generators': [1, 48, 96], 'label': '1152.155799.144.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.c1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60968487
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '48.k1.a1', '72.b1.a1', '72.i1.a1', '72.j1.a1'], 'contains': ['288.c1.a1', '288.f1.a1', '288.g1.a1', '288.o1.a1', '288.o1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6389, -1, 5827, -1, 3349, -1, 2987, -1], 'generators': [1, 2, 48], 'label': '1152.155799.144.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1.a1', 'old_label': '144.d1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968488
    {'ambient': '1152.155799', 'aut_centralizer_order': 384, 'aut_label': '144.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.h1.a1', '72.c1.a1', '72.i1.a1', '72.k1.a1', '72.l1.a1', '72.m1.a1'], 'contains': ['288.a1.a1', '288.c1.a1', '288.i1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6933, -1, 7215, -1, 6297, -1, 6813, -1], 'generators': [1, 24], 'label': '1152.155799.144.e1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '144.e1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968489
    {'ambient': '1152.155799', 'aut_centralizer_order': 128, 'aut_label': '144.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.l1.a1', '72.c1.a1', '72.d1.a1', '72.j1.a1', '72.n1.a1'], 'contains': ['288.c1.a1', '288.h1.a1', '288.j1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7741, -1, 7698, -1, 4878, -1, 5503, -1], 'generators': [1, 120], 'label': '1152.155799.144.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.f1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968490
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '144.g1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '72.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '48.m1.a1', '72.f1.a1', '72.k1.a1', '72.n1.a1'], 'contains': ['288.c1.a1', '288.k1.a1', '288.l1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8077, -1, 8285, -1, 5135, -1, 6514, -1], 'generators': [1, 6], 'label': '1152.155799.144.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1.a1', 'old_label': '144.g1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968491
    {'ambient': '1152.155799', 'aut_centralizer_order': 128, 'aut_label': '144.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.n1.a1', '72.h1.a1', '72.o1.a1', '72.p1.a1', '72.q1.a1', '72.r1.a1', '72.s1.a1', '72.t1.a1'], 'contains': ['288.d1.a1', '288.e1.a1', '288.q1.a1', '288.q1.b1', '288.v1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3852, -1, 3895, -1, 2504, -1, 3345, -1], 'generators': [577, 48, 96], 'label': '1152.155799.144.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.h1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968492
    {'ambient': '1152.155799', 'aut_centralizer_order': 12, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '48.ca1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '4.j1.a1'], 'contains': ['16.d1.a1', '16.k1.a1', '16.l1.a1', '24.b1.a1', '24.i1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4503, -1, 5928, -1, 9484, -1, 4287, -1], 'generators': [1, 384, 48, 12, 32, 24], 'label': '1152.155799.8.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '8.f1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968493
    {'ambient': '1152.155799', 'aut_centralizer_order': 192, 'aut_label': '144.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '24.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.a1', '72.b1.a1', '72.o1.a1', '72.u1.a1', '72.v1.a1', '72.w1.a1', '72.x1.a1', '72.bs1.a1'], 'contains': ['288.d1.a1', '288.f1.a1', '288.r1.a1', '288.w1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3219, -1, 3563, -1, 2106, -1, 2932, -1], 'generators': [2, 48, 576], 'label': '1152.155799.144.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '144.i1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968494
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '144.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1.a1', '72.b1.a1', '72.p1.a1', '72.u1.a1', '72.y1.a1', '72.z1.a1', '72.ba1.a1', '72.bt1.a1'], 'contains': ['288.d1.a1', '288.g1.a1', '288.s1.a1', '288.x1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2740, -1, 3472, -1, 2049, -1, 2841, -1], 'generators': [3, 48, 576], 'label': '1152.155799.144.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '144.j1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968495
    {'ambient': '1152.155799', 'aut_centralizer_order': 768, 'aut_label': '144.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.q1.a1', '72.a1.a1', '72.c1.a1', '72.q1.a1', '72.x1.a1', '72.ba1.a1', '72.bb1.a1', '72.bc1.a1', '72.bd1.a1', '72.be1.a1', '72.bf1.a1', '72.bg1.a1', '72.bh1.a1', '72.bi1.a1', '72.bj1.a1', '72.bk1.a1'], 'contains': ['288.a1.a1', '288.d1.a1', '288.h1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6640, -1, 6856, -1, 6177, -1, 6572, -1], 'generators': [24, 96], 'label': '1152.155799.144.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.k1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968496
    {'ambient': '1152.155799', 'aut_centralizer_order': 384, 'aut_label': '144.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.r1.a1', '72.a1.a1', '72.d1.a1', '72.r1.a1', '72.v1.a1', '72.y1.a1', '72.bl1.a1', '72.bm1.a1'], 'contains': ['288.d1.a1', '288.h1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4221, -1, 4319, -1, 3611, -1, 5036, -1], 'generators': [600, 96], 'label': '1152.155799.144.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.l1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968497
    {'ambient': '1152.155799', 'aut_centralizer_order': 256, 'aut_label': '144.m1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.s1.a1', '72.c1.a1', '72.r1.a1', '72.u1.a1', '72.bn1.a1', '72.bo1.a1', '72.bp1.a1', '72.bu1.a1'], 'contains': ['288.d1.a1', '288.i1.a1', '288.j1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3902, -1, 4103, -1, 3552, -1, 5093, -1], 'generators': [25, 96], 'label': '1152.155799.144.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.m1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968498
    {'ambient': '1152.155799', 'aut_centralizer_order': 128, 'aut_label': '144.n1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.t1.a1', '72.d1.a1', '72.q1.a1', '72.w1.a1', '72.z1.a1', '72.bq1.a1', '72.br1.a1', '72.bu1.a1'], 'contains': ['288.d1.a1', '288.j1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4123, -1, 4225, -1, 3114, -1, 4862, -1], 'generators': [601, 96], 'label': '1152.155799.144.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.n1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.n1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968499
    {'ambient': '1152.155799', 'aut_centralizer_order': 192, 'aut_label': '144.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '24.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.u1.a1', '72.e1.a1', '72.p1.a1', '72.v1.a1', '72.z1.a1', '72.bb1.a1', '72.bn1.a1', '72.bs1.a1'], 'contains': ['288.d1.a1', '288.t1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2509, -1, 3132, -1, 1958, -1, 2361, -1], 'generators': [98, 48], 'label': '1152.155799.144.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '144.o1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.o1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968500
    {'ambient': '1152.155799', 'aut_centralizer_order': 192, 'aut_label': '144.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.v1.a1', '72.f1.a1', '72.s1.a1', '72.bc1.a1', '72.bl1.a1', '72.bo1.a1', '72.bq1.a1', '72.bv1.a1'], 'contains': ['288.d1.a1', '288.k1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5007, -1, 5132, -1, 4337, -1, 5986, -1], 'generators': [6, 96], 'label': '1152.155799.144.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '144.p1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.p1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968501
    {'ambient': '1152.155799', 'aut_centralizer_order': 192, 'aut_label': '144.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '24.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.w1.a1', '72.g1.a1', '72.t1.a1', '72.bd1.a1', '72.bl1.a1', '72.bp1.a1', '72.br1.a1', '72.bv1.a1'], 'contains': ['288.d1.a1', '288.y1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4621, -1, 4866, -1, 3882, -1, 5388, -1], 'generators': [582, 96], 'label': '1152.155799.144.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '144.q1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.q1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968502
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '144.r1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.x1.a1', '72.g1.a1', '72.s1.a1', '72.be1.a1', '72.bm1.a1', '72.bp1.a1', '72.bq1.a1', '72.bw1.a1'], 'contains': ['288.d1.a1', '288.z1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4489, -1, 4671, -1, 3742, -1, 5229, -1], 'generators': [583, 96], 'label': '1152.155799.144.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '144.r1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.r1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968503
    {'ambient': '1152.155799', 'aut_centralizer_order': 24, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.h1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '16.n1.a1', '24.by1.a1', '24.bz1.a1', '32.c1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [600, -1, 937, -1, 1397, -1, 1498, -1], 'generators': [2, 576, 672, 48, 384, 32], 'label': '1152.155799.8.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.g1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 60968504
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '144.s1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.y1.a1', '72.e1.a1', '72.o1.a1', '72.w1.a1', '72.y1.a1', '72.bf1.a1', '72.bn1.a1', '72.bt1.a1'], 'contains': ['288.d1.a1', '288.u1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2411, -1, 3182, -1, 1887, -1, 2420, -1], 'generators': [99, 48], 'label': '1152.155799.144.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '144.s1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.s1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968505
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '144.t1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '72.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.z1.a1', '72.f1.a1', '72.t1.a1', '72.bg1.a1', '72.bm1.a1', '72.bo1.a1', '72.br1.a1', '72.bw1.a1'], 'contains': ['288.d1.a1', '288.l1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4833, -1, 4794, -1, 4226, -1, 5877, -1], 'generators': [7, 96], 'label': '1152.155799.144.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1.a1', 'old_label': '144.t1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.t1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968506
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '144.u1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bb1.a1', '72.b1.a1', '72.bx1.a1', '72.by1.a1'], 'contains': ['288.e1.a1', '288.f1.a1', '288.g1.a1', '288.ba1.a1', '288.ba1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7043, -1, 7460, -1, 3930, -1, 3379, -1], 'generators': [577, 2, 48], 'label': '1152.155799.144.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1.a1', 'old_label': '144.u1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.u1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968507
    {'ambient': '1152.155799', 'aut_centralizer_order': 128, 'aut_label': '144.v1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bc1.a1', '72.c1.a1', '72.q1.a1', '72.bx1.a1', '72.bz1.a1', '72.ca1.a1', '72.cb1.a1', '72.cc1.a1'], 'contains': ['288.a1.a1', '288.e1.a1', '288.j1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7922, -1, 7546, -1, 6585, -1, 7262, -1], 'generators': [97, 24], 'label': '1152.155799.144.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.v1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.v1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968508
    {'ambient': '1152.155799', 'aut_centralizer_order': 128, 'aut_label': '144.w1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bd1.a1', '72.c1.a1', '72.r1.a1', '72.by1.a1', '72.cd1.a1'], 'contains': ['288.e1.a1', '288.h1.a1', '288.i1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7433, -1, 7774, -1, 4818, -1, 5446, -1], 'generators': [97, 120], 'label': '1152.155799.144.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.w1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.w1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968509
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '144.x1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.be1.a1', '72.d1.a1', '72.q1.a1', '72.r1.a1'], 'contains': ['288.e1.a1', '288.h1.a1', '288.j1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4404, -1, 4606, -1, 4010, -1, 5286, -1], 'generators': [577, 120], 'label': '1152.155799.144.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1.a1', 'old_label': '144.x1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.x1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60968510
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '144.y1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '72.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bf1.a1', '72.f1.a1', '72.bz1.a1', '72.cd1.a1'], 'contains': ['288.e1.a1', '288.k1.a1', '288.l1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9076, -1, 9045, -1, 5226, -1, 6753, -1], 'generators': [97, 6], 'label': '1152.155799.144.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1.a1', 'old_label': '144.y1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.y1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968511
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '144.z1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bg1.a1', '48.bk1.a1', '72.i1.a1', '72.u1.a1', '72.by1.a1'], 'contains': ['288.f1.a1', '288.g1.a1', '288.i1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6351, -1, 6755, -1, 3696, -1, 3804, -1], 'generators': [25, 2], 'label': '1152.155799.144.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1.a1', 'old_label': '144.z1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.z1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968512
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '144.ba1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bh1.a1', '72.j1.a1', '72.u1.a1', '72.bx1.a1'], 'contains': ['288.f1.a1', '288.g1.a1', '288.j1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7700, -1, 7144, -1, 3964, -1, 4157, -1], 'generators': [601, 2], 'label': '1152.155799.144.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1.a1', 'old_label': '144.ba1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968513
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '144.bb1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bi1.a1', '48.bl1.a1', '72.i1.a1', '72.x1.a1', '72.bx1.a1', '72.ce1.a1', '72.cf1.a1', '72.cg1.a1', '72.ch1.a1'], 'contains': ['288.a1.a1', '288.f1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8324, -1, 8062, -1, 6663, -1, 7179, -1], 'generators': [2, 24], 'label': '1152.155799.144.bb1.a1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '144.bb1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60968514
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 16, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.h1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '16.o1.a1', '24.ca1.a1', '24.cb1.a1', '24.cc1.a1', '32.d1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [995, -1, 1070, -1, 1179, -1, 1562, -1], 'generators': [3, 576, 672, 48, 32, 384], 'label': '1152.155799.8.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.h1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 60968515
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '144.bc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bj1.a1', '72.j1.a1', '72.x1.a1', '72.by1.a1'], 'contains': ['288.f1.a1', '288.h1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7539, -1, 7356, -1, 4955, -1, 4451, -1], 'generators': [2, 600], 'label': '1152.155799.144.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '144.bc1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60968516
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '144.bd1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bm1.a1', '48.bo1.a1', '48.bp1.a1', '72.i1.a1', '72.ba1.a1', '72.bx1.a1', '72.ci1.a1', '72.cj1.a1', '72.ck1.a1', '72.cl1.a1'], 'contains': ['288.a1.a1', '288.g1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7783, -1, 8350, -1, 6631, -1, 6857, -1], 'generators': [3, 24], 'label': '1152.155799.144.bd1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '144.bd1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60968517
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '144.be1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bn1.a1', '72.j1.a1', '72.ba1.a1', '72.by1.a1'], 'contains': ['288.g1.a1', '288.h1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7344, -1, 7660, -1, 4923, -1, 4386, -1], 'generators': [3, 600], 'label': '1152.155799.144.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '144.be1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.be1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60968518
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '144.bf1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bq1.a1', '48.by1.a1', '72.k1.a1', '72.bc1.a1', '72.bz1.a1', '72.ce1.a1', '72.cf1.a1', '72.ci1.a1', '72.cj1.a1'], 'contains': ['288.a1.a1', '288.k1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8878, -1, 8798, -1, 7821, -1, 8084, -1], 'generators': [6, 24], 'label': '1152.155799.144.bf1.a1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '144.bf1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60968519
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '144.bg1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.br1.a1', '48.bz1.a1', '48.cd1.a1', '72.k1.a1', '72.bg1.a1', '72.bz1.a1', '72.cg1.a1', '72.ch1.a1', '72.ck1.a1', '72.cl1.a1'], 'contains': ['288.a1.a1', '288.l1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8211, -1, 8441, -1, 7204, -1, 7811, -1], 'generators': [7, 24], 'label': '1152.155799.144.bg1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '144.bg1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60968520
    {'ambient': '1152.155799', 'aut_centralizer_order': 384, 'aut_label': '144.bh1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bs1.a1', '72.m1.a1', '72.bh1.a1', '72.bi1.a1', '72.cb1.a1', '72.cc1.a1', '72.cf1.a1', '72.cl1.a1'], 'contains': ['288.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8658, -1, 8519, -1, 7789, -1, 9059, -1], 'generators': [108], 'label': '1152.155799.144.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.bh1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968521
    {'ambient': '1152.155799', 'aut_centralizer_order': 384, 'aut_label': '144.bi1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '48.cb1.a1', '72.l1.a1', '72.bj1.a1', '72.cb1.a1', '72.cg1.a1', '72.ci1.a1'], 'contains': ['288.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7494, -1, 8178, -1, 8837, -1, 8489, -1], 'generators': [13], 'label': '1152.155799.144.bi1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '48.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '144.bi1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968522
    {'ambient': '1152.155799', 'aut_centralizer_order': 128, 'aut_label': '144.bj1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bt1.a1', '72.m1.a1', '72.bj1.a1', '72.bk1.a1', '72.ca1.a1', '72.cc1.a1', '72.ch1.a1', '72.cj1.a1'], 'contains': ['288.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8295, -1, 7597, -1, 7743, -1, 9097, -1], 'generators': [109], 'label': '1152.155799.144.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.bj1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968523
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '144.bk1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bu1.a1', '72.n1.a1', '72.bc1.a1', '72.cd1.a1'], 'contains': ['288.h1.a1', '288.k1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9117, -1, 8992, -1, 5694, -1, 7342, -1], 'generators': [6, 120], 'label': '1152.155799.144.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '144.bk1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60968524
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '144.bl1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.3', 'aut_weyl_index': 576, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bv1.a1', '72.n1.a1', '72.bg1.a1', '72.cd1.a1'], 'contains': ['288.h1.a1', '288.l1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9035, -1, 8902, -1, 5533, -1, 7307, -1], 'generators': [7, 120], 'label': '1152.155799.144.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '144.bl1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 60968525
    {'ambient': '1152.155799', 'aut_centralizer_order': 24, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.i1.a1', '4.l1.a1'], 'contains': ['16.a1.a1', '24.cd1.a1', '24.cg1.a1', '32.g1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1444, -1, 1918, -1, 3117, -1, 3059, -1], 'generators': [6, 576, 96, 384, 48, 32], 'label': '1152.155799.8.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.i1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 60968526
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '144.bm1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bw1.a1', '48.cc1.a1', '72.k1.a1', '72.bo1.a1', '72.cd1.a1'], 'contains': ['288.i1.a1', '288.k1.a1', '288.l1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8159, -1, 8323, -1, 5181, -1, 6709, -1], 'generators': [25, 6], 'label': '1152.155799.144.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1.a1', 'old_label': '144.bm1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968527
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '144.bn1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bx1.a1', '72.n1.a1', '72.bo1.a1', '72.bz1.a1'], 'contains': ['288.j1.a1', '288.k1.a1', '288.l1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9147, -1, 9082, -1, 5272, -1, 6887, -1], 'generators': [121, 6], 'label': '1152.155799.144.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1.a1', 'old_label': '144.bn1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968528
    {'ambient': '1152.155799', 'aut_centralizer_order': 128, 'aut_label': '144.bo1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cg1.a1', '72.h1.a1', '72.cm1.a1'], 'contains': ['288.m1.a1', '288.n1.a1', '288.p1.a1', '288.q1.b1', '288.v1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1576, -1, 2040, -1, 1133, -1, 1567, -1], 'generators': [1, 624, 96], 'label': '1152.155799.144.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.bo1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968529
    {'ambient': '1152.155799', 'aut_centralizer_order': 128, 'aut_label': '144.bo1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cg1.b1', '72.h1.a1', '72.cm1.b1'], 'contains': ['288.m1.b1', '288.n1.b1', '288.p1.a1', '288.q1.a1', '288.v1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1576, -1, 2070, -1, 1133, -1, 1533, -1], 'generators': [577, 624, 96], 'label': '1152.155799.144.bo1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.bo1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bo1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968530
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '144.bp1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ch1.a1', '72.b1.a1', '72.cm1.a1', '72.cn1.a1'], 'contains': ['288.m1.a1', '288.o1.a1', '288.r1.a1', '288.s1.a1', '288.ba1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1413, -1, 1378, -1, 1097, -1, 1288, -1], 'generators': [1, 2, 576], 'label': '1152.155799.144.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1.a1', 'old_label': '144.bp1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968531
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '144.bp1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ch1.b1', '72.b1.a1', '72.cm1.b1', '72.cn1.b1'], 'contains': ['288.m1.b1', '288.o1.b1', '288.r1.a1', '288.s1.a1', '288.ba1.b1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1413, -1, 1888, -1, 1097, -1, 1223, -1], 'generators': [49, 2, 576], 'label': '1152.155799.144.bp1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1.a1', 'old_label': '144.bp1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bp1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968532
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '144.bq1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ci1.a1', '72.e1.a1', '72.cm1.a1', '72.cn1.a1'], 'contains': ['288.m1.a1', '288.t1.a1', '288.u1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [961, -1, 1192, -1, 877, -1, 921, -1], 'generators': [1, 98], 'label': '1152.155799.144.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1.a1', 'old_label': '144.bq1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968533
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '144.bq1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ci1.b1', '72.e1.a1', '72.cm1.b1', '72.cn1.b1'], 'contains': ['288.m1.b1', '288.t1.a1', '288.u1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [961, -1, 1338, -1, 877, -1, 826, -1], 'generators': [49, 98], 'label': '1152.155799.144.bq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1.a1', 'old_label': '144.bq1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bq1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968534
    {'ambient': '1152.155799', 'aut_centralizer_order': 128, 'aut_label': '144.br1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.cf1.a1', '72.h1.a1', '72.cn1.a1'], 'contains': ['288.b1.a1', '288.m1.a1', '288.q1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [435, -1, 416, -1, 830, -1, 1158, -1], 'generators': [1, 96, 576], 'label': '1152.155799.144.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '144.br1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.br1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968535
    {'ambient': '1152.155799', 'aut_centralizer_order': 128, 'aut_label': '144.br1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.b1', '48.cf1.b1', '72.h1.a1', '72.cn1.b1'], 'contains': ['288.b1.a1', '288.m1.b1', '288.q1.b1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [435, -1, 762, -1, 830, -1, 723, -1], 'generators': [49, 96, 576], 'label': '1152.155799.144.br1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '144.br1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.br1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968536
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 16, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.i1.a1', '4.l1.a1'], 'contains': ['16.a1.a1', '24.ce1.a1', '24.ch1.a1', '24.cj1.a1', '32.h1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1754, -1, 2331, -1, 2960, -1, 3202, -1], 'generators': [7, 576, 96, 48, 32, 384], 'label': '1152.155799.8.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.j1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 60968537
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '144.bs1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cj1.a1', '72.b1.a1'], 'contains': ['288.n1.a1', '288.o1.a1', '288.w1.a1', '288.x1.a1', '288.ba1.b1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2867, -1, 3029, -1, 1572, -1, 2466, -1], 'generators': [1, 2, 624], 'label': '1152.155799.144.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '144.bs1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968538
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '144.bs1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cj1.b1', '72.b1.a1'], 'contains': ['288.n1.b1', '288.o1.b1', '288.w1.a1', '288.x1.a1', '288.ba1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2867, -1, 3237, -1, 1572, -1, 2501, -1], 'generators': [577, 2, 624], 'label': '1152.155799.144.bs1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '144.bs1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bs1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968539
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '144.bt1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ck1.a1', '72.g1.a1'], 'contains': ['288.n1.a1', '288.y1.a1', '288.z1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4290, -1, 4722, -1, 2866, -1, 4535, -1], 'generators': [1, 582], 'label': '1152.155799.144.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1.a1', 'old_label': '144.bt1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968540
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '144.bt1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ck1.b1', '72.g1.a1'], 'contains': ['288.n1.b1', '288.y1.a1', '288.z1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4290, -1, 4500, -1, 2866, -1, 4629, -1], 'generators': [97, 582], 'label': '1152.155799.144.bt1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1.a1', 'old_label': '144.bt1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bt1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968541
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '144.bu1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cl1.a1', '72.bs1.a1', '72.cm1.a1', '72.cm1.b1'], 'contains': ['288.p1.a1', '288.r1.a1', '288.t1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1444, -1, 1725, -1, 1063, -1, 1191, -1], 'generators': [2, 144], 'label': '1152.155799.144.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '144.bu1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968542
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '144.bv1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cm1.a1', '72.bt1.a1', '72.cm1.a1', '72.cm1.b1'], 'contains': ['288.p1.a1', '288.s1.a1', '288.u1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1492, -1, 1660, -1, 940, -1, 1095, -1], 'generators': [3, 144], 'label': '1152.155799.144.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1.a1', 'old_label': '144.bv1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968543
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '144.bw1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cn1.a1', '72.o1.a1', '72.cm1.b1', '72.cn1.a1'], 'contains': ['288.q1.a1', '288.r1.a1', '288.u1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1153, -1, 1831, -1, 641, -1, 1026, -1], 'generators': [97, 2], 'label': '1152.155799.144.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1.a1', 'old_label': '144.bw1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968544
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '144.bw1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cn1.b1', '72.o1.a1', '72.cm1.a1', '72.cn1.b1'], 'contains': ['288.q1.b1', '288.r1.a1', '288.u1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1153, -1, 1286, -1, 641, -1, 1126, -1], 'generators': [145, 2], 'label': '1152.155799.144.bw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1.a1', 'old_label': '144.bw1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bw1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968545
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '144.bx1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.co1.a1', '72.p1.a1', '72.cm1.b1', '72.cn1.a1'], 'contains': ['288.q1.a1', '288.s1.a1', '288.t1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1018, -1, 1478, -1, 764, -1, 965, -1], 'generators': [97, 98], 'label': '1152.155799.144.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1.a1', 'old_label': '144.bx1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968546
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '144.bx1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.co1.b1', '72.p1.a1', '72.cm1.a1', '72.cn1.b1'], 'contains': ['288.q1.b1', '288.s1.a1', '288.t1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1018, -1, 1245, -1, 764, -1, 995, -1], 'generators': [145, 98], 'label': '1152.155799.144.bx1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1.a1', 'old_label': '144.bx1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bx1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968547
    {'ambient': '1152.155799', 'aut_centralizer_order': 6, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '4.j1.a1'], 'contains': ['16.g1.a1', '16.i1.a1', '16.k1.a1', '24.cr1.a1', '24.cv1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3458, -1, 5566, -1, 9212, -1, 3882, -1], 'generators': [2, 32, 48, 12, 384, 24], 'label': '1152.155799.8.k1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '8.k1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.a1', 'subgroup_fusion': None, 'weyl_group': '48.36'}
  • id: 60968548
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '144.by1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cp1.a1', '48.cq1.a1', '72.bs1.a1', '72.cn1.a1', '72.cn1.b1'], 'contains': ['288.b1.a1', '288.r1.a1', '288.t1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [282, -1, 501, -1, 530, -1, 690, -1], 'generators': [2, 96], 'label': '1152.155799.144.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '144.by1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.by1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968549
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '144.bz1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cr1.a1', '48.cs1.a1', '48.ct1.a1', '72.bt1.a1', '72.cn1.a1', '72.cn1.b1'], 'contains': ['288.b1.a1', '288.s1.a1', '288.u1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [593, -1, 702, -1, 357, -1, 660, -1], 'generators': [3, 96], 'label': '1152.155799.144.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1.a1', 'old_label': '144.bz1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60968550
    {'ambient': '1152.155799', 'aut_centralizer_order': 2304, 'aut_label': '192.a1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '2.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.a1.a1', '96.b1.a1', '96.c1.a1', '96.g1.a1', '96.h1.a1', '96.i1.a1', '96.k1.a1', '96.n1.a1', '96.o1.a1', '96.p1.a1', '96.q1.a1'], 'contains': ['384.a1.a1', '576.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7561, 3871, 7857, 3154, 3508, 4650, 4024, 3505], 'generators': [48, 384], 'label': '1152.155799.192.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '192.a1.a1', 'normal_contained_in': ['48.b1.a1', '96.a1.a1', '96.b1.a1', '96.c1.a1'], 'normal_contains': ['384.a1.a1', '576.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.a1.a1', 'projective_image': '576.8312', 'quotient_action_image': '2.1', 'quotient_action_kernel': '96.187', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968551
    {'ambient': '1152.155799', 'aut_centralizer_order': 384, 'aut_label': '192.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '6.b1.a1', 'complements': ['6.b1.a1', '6.v1.a1', '6.w1.a1', '6.r1.a1', '6.u1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.b1.a1', '96.a1.a1', '96.y1.a1', '96.z1.a1', '96.ba1.a1'], 'contains': ['384.a1.a1', '576.b1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1809, 2471, 1976, 1286, 1353, 3866, 1698, 2169], 'generators': [1, 384], 'label': '1152.155799.192.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '192.b1.a1', 'normal_contained_in': ['48.f1.a1', '96.a1.a1'], 'normal_contains': ['384.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.b1.a1', 'projective_image': '1152.155799', 'quotient_action_image': '1.1', 'quotient_action_kernel': '192.960', 'quotient_action_kernel_order': 192, 'quotient_fusion': None, 'short_label': '192.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968552
    {'ambient': '1152.155799', 'aut_centralizer_order': 384, 'aut_label': '192.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '6.b1.a1', 'complements': ['6.b1.a1', '6.v1.a1', '6.w1.a1', '6.r1.a1', '6.u1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.b1.b1', '96.a1.a1', '96.y1.b1', '96.z1.b1', '96.ba1.b1'], 'contains': ['384.a1.a1', '576.b1.b1'], 'core': '192.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1809, 2471, 2262, 1967, 1353, 3866, 1606, 1787], 'generators': [49, 384], 'label': '1152.155799.192.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '192.b1.b1', 'normal_contained_in': ['48.f1.b1', '96.a1.a1'], 'normal_contains': ['384.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.b1.b1', 'projective_image': '1152.155799', 'quotient_action_image': '1.1', 'quotient_action_kernel': '192.960', 'quotient_action_kernel_order': 192, 'quotient_fusion': None, 'short_label': '192.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968553
    {'ambient': '1152.155799', 'aut_centralizer_order': 576, 'aut_label': '192.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '64.a1.a1', '96.f1.a1', '96.j1.a1', '96.l1.a1', '96.r1.a1', '96.s1.a1', '96.t1.a1', '96.u1.a1'], 'contains': ['384.b1.a1', '576.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1154, -1, 1045, -1, 2727, -1, 1980, -1], 'generators': [48, 32], 'label': '1152.155799.192.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '192.c1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968554
    {'ambient': '1152.155799', 'aut_centralizer_order': 288, 'aut_label': '192.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ba1.a1', '64.a1.a1', '96.m1.a1', '96.v1.a1', '96.w1.a1'], 'contains': ['384.c1.a1', '576.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2271, -1, 2711, -1, 2668, -1, 2048, -1], 'generators': [48, 416], 'label': '1152.155799.192.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.n1.a1', 'old_label': '192.d1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968555
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '192.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '24.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cf1.a1', '64.b1.a1', '96.f1.a1', '96.x1.a1'], 'contains': ['384.b1.a1', '576.b1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [157, -1, 67, -1, 1290, -1, 635, -1], 'generators': [1, 32], 'label': '1152.155799.192.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '192.e1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968556
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '192.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '24.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cf1.b1', '64.b1.b1', '96.f1.a1', '96.x1.b1'], 'contains': ['384.b1.a1', '576.b1.b1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [157, -1, 375, -1, 1290, -1, 442, -1], 'generators': [49, 32], 'label': '1152.155799.192.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '192.e1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.e1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968557
    {'ambient': '1152.155799', 'aut_centralizer_order': 768, 'aut_label': '192.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '6.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1.a1', '96.g1.a1', '96.y1.a1', '96.y1.b1', '96.bb1.a1', '96.bc1.a1', '96.bc1.b1', '96.bd1.a1', '96.be1.a1', '96.bf1.a1', '96.bg1.a1'], 'contains': ['384.a1.a1', '576.c1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1303, -1, 1512, -1, 821, -1, 1402, -1], 'generators': [96, 384], 'label': '1152.155799.192.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '192.f1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968558
    {'ambient': '1152.155799', 'aut_centralizer_order': 2, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '576.8553', 'aut_weyl_index': 8, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '4.j1.a1'], 'contains': ['16.g1.a1', '16.j1.a1', '16.l1.a1', '24.ct1.a1', '24.cw1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4190, -1, 5265, -1, 9092, -1, 3824, -1], 'generators': [13, 384, 32, 2, 24, 48], 'label': '1152.155799.8.l1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '8.l1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.a1', 'subgroup_fusion': None, 'weyl_group': '144.144'}
  • id: 60968559
    {'ambient': '1152.155799', 'aut_centralizer_order': 768, 'aut_label': '192.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '6.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.g1.a1', '96.z1.a1', '96.z1.b1', '96.bb1.a1', '96.bi1.a1', '96.bj1.a1', '96.bk1.a1', '96.bl1.a1', '96.bm1.a1'], 'contains': ['384.a1.a1', '576.d1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3063, -1, 3749, -1, 1592, -1, 2603, -1], 'generators': [144, 384], 'label': '1152.155799.192.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '192.g1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968560
    {'ambient': '1152.155799', 'aut_centralizer_order': 128, 'aut_label': '192.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '18.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1.a1', '96.y1.a1', '96.z1.b1', '96.bc1.a1', '96.bi1.a1', '96.bn1.a1'], 'contains': ['384.a1.a1', '576.e1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1927, -1, 2373, -1, 1452, -1, 1828, -1], 'generators': [97, 384], 'label': '1152.155799.192.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '192.h1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968561
    {'ambient': '1152.155799', 'aut_centralizer_order': 128, 'aut_label': '192.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '18.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1.a1', '96.y1.b1', '96.z1.a1', '96.bc1.b1', '96.bi1.a1', '96.bn1.b1'], 'contains': ['384.a1.a1', '576.e1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1927, -1, 2289, -1, 1452, -1, 1797, -1], 'generators': [145, 384], 'label': '1152.155799.192.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '192.h1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.h1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968562
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '192.i1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '48.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.c1.a1', '96.i1.a1', '96.ba1.a1', '96.ba1.b1', '96.bd1.a1', '96.bj1.a1', '96.bn1.a1', '96.bn1.b1'], 'contains': ['384.a1.a1', '576.f1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1882, -1, 2317, -1, 1421, -1, 1667, -1], 'generators': [2, 384], 'label': '1152.155799.192.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.j1.a1', 'old_label': '192.i1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968563
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '192.j1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cq1.a1', '64.c1.a1', '96.j1.a1', '96.x1.a1', '96.x1.b1'], 'contains': ['384.b1.a1', '576.f1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [226, -1, 280, -1, 1258, -1, 530, -1], 'generators': [2, 32], 'label': '1152.155799.192.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1.a1', 'old_label': '192.j1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968564
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '192.k1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.d1.a1', '96.k1.a1', '96.ba1.a1', '96.ba1.b1', '96.be1.a1', '96.bk1.a1', '96.bn1.a1', '96.bn1.b1'], 'contains': ['384.a1.a1', '576.g1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1764, -1, 2222, -1, 1321, -1, 1637, -1], 'generators': [3, 384], 'label': '1152.155799.192.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.j1.a1', 'old_label': '192.k1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968565
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '192.l1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cs1.a1', '64.d1.a1', '96.l1.a1', '96.x1.a1', '96.x1.b1'], 'contains': ['384.b1.a1', '576.g1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [70, -1, 214, -1, 1190, -1, 499, -1], 'generators': [3, 32], 'label': '1152.155799.192.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.g1.a1', 'old_label': '192.l1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.l1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968566
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '192.m1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ct1.a1', '64.d1.a1', '96.m1.a1'], 'contains': ['384.c1.a1', '576.g1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [671, -1, 843, -1, 1158, -1, 598, -1], 'generators': [3, 416], 'label': '1152.155799.192.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.m1.a1', 'old_label': '192.m1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.m1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968567
    {'ambient': '1152.155799', 'aut_centralizer_order': 2304, 'aut_label': '288.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '96.r1.a1', '96.v1.a1', '144.b1.a1', '144.e1.a1', '144.k1.a1', '144.v1.a1', '144.bb1.a1', '144.bd1.a1', '144.bf1.a1', '144.bg1.a1', '144.bh1.a1', '144.bi1.a1', '144.bj1.a1'], 'contains': ['576.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7783, 5707, 7673, 6227, 6663, 6295, 7179, 5154], 'generators': [24], 'label': '1152.155799.288.a1.a1', 'mobius_quo': 0, 'mobius_sub': 288, 'normal_closure': '288.a1.a1', 'normal_contained_in': ['72.a1.a1', '96.b1.a1', '144.b1.a1'], 'normal_contains': ['576.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.a1.a1', 'projective_image': '576.8312', 'quotient_action_image': '2.1', 'quotient_action_kernel': '144.190', 'quotient_action_kernel_order': 144, 'quotient_fusion': None, 'short_label': '288.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968568
    {'ambient': '1152.155799', 'aut_centralizer_order': 768, 'aut_label': '288.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 768, 'centralizer': '6.a1.a1', 'complements': ['4.j1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['96.d1.a1', '96.e1.a1', '96.bh1.a1', '144.a1.a1', '144.br1.a1', '144.br1.b1', '144.by1.a1', '144.bz1.a1'], 'contains': ['576.c1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [495, 1473, 702, 2572, 507, 3107, 723, 4162], 'generators': [96, 576], 'label': '1152.155799.288.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '288.b1.a1', 'normal_contained_in': ['96.d1.a1', '96.e1.a1', '144.a1.a1'], 'normal_contains': ['1152.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.b1.a1', 'projective_image': '1152.155799', 'quotient_action_image': '6.1', 'quotient_action_kernel': '48.4', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '288.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60968569
    {'ambient': '1152.155799', 'aut_centralizer_order': 2, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '576.8553', 'aut_weyl_index': 8, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '4.j1.a1'], 'contains': ['16.h1.a1', '16.i1.a1', '16.l1.a1', '24.cx1.a1', '24.db1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4239, -1, 5483, -1, 9146, -1, 3961, -1], 'generators': [13, 384, 32, 6, 24, 48], 'label': '1152.155799.8.m1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '8.m1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1.a1', 'subgroup_fusion': None, 'weyl_group': '144.144'}
  • id: 60968570
    {'ambient': '1152.155799', 'aut_centralizer_order': 768, 'aut_label': '288.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '96.f1.a1', '144.c1.a1', '144.d1.a1', '144.e1.a1', '144.f1.a1', '144.g1.a1'], 'contains': ['576.a1.a1', '576.b1.a1', '576.b1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6884, -1, 7075, -1, 3474, -1, 3688, -1], 'generators': [1, 48], 'label': '1152.155799.288.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '288.c1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60968571
    {'ambient': '1152.155799', 'aut_centralizer_order': 1536, 'aut_label': '288.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.g1.a1', '144.a1.a1', '144.c1.a1', '144.h1.a1', '144.i1.a1', '144.j1.a1', '144.k1.a1', '144.l1.a1', '144.m1.a1', '144.n1.a1', '144.o1.a1', '144.p1.a1', '144.q1.a1', '144.r1.a1', '144.s1.a1', '144.t1.a1'], 'contains': ['576.a1.a1', '576.c1.a1', '576.d1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3976, -1, 4103, -1, 2556, -1, 3653, -1], 'generators': [48, 96], 'label': '1152.155799.288.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '288.d1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60968572
    {'ambient': '1152.155799', 'aut_centralizer_order': 256, 'aut_label': '288.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1.a1', '144.c1.a1', '144.h1.a1', '144.u1.a1', '144.v1.a1', '144.w1.a1', '144.x1.a1', '144.y1.a1'], 'contains': ['576.a1.a1', '576.e1.a1', '576.e1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7051, -1, 7173, -1, 3650, -1, 4056, -1], 'generators': [97, 48], 'label': '1152.155799.288.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '288.e1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60968573
    {'ambient': '1152.155799', 'aut_centralizer_order': 192, 'aut_label': '288.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '24.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i1.a1', '96.j1.a1', '144.d1.a1', '144.i1.a1', '144.u1.a1', '144.z1.a1', '144.ba1.a1', '144.bb1.a1', '144.bc1.a1'], 'contains': ['576.a1.a1', '576.f1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6989, -1, 7032, -1, 3438, -1, 3379, -1], 'generators': [2, 48], 'label': '1152.155799.288.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1.a1', 'old_label': '288.f1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968574
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '288.g1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.k1.a1', '96.l1.a1', '96.m1.a1', '144.d1.a1', '144.j1.a1', '144.u1.a1', '144.z1.a1', '144.ba1.a1', '144.bd1.a1', '144.be1.a1'], 'contains': ['576.a1.a1', '576.g1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6533, -1, 6847, -1, 3392, -1, 3300, -1], 'generators': [3, 48], 'label': '1152.155799.288.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1.a1', 'old_label': '288.g1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968575
    {'ambient': '1152.155799', 'aut_centralizer_order': 768, 'aut_label': '288.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.n1.a1', '144.f1.a1', '144.k1.a1', '144.l1.a1', '144.w1.a1', '144.x1.a1', '144.bc1.a1', '144.be1.a1', '144.bk1.a1', '144.bl1.a1'], 'contains': ['576.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7433, -1, 7632, -1, 4878, -1, 5341, -1], 'generators': [120], 'label': '1152.155799.288.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '288.h1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968576
    {'ambient': '1152.155799', 'aut_centralizer_order': 768, 'aut_label': '288.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.c1.a1', '96.s1.a1', '144.e1.a1', '144.m1.a1', '144.w1.a1', '144.z1.a1', '144.bm1.a1'], 'contains': ['576.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6854, -1, 7117, -1, 3744, -1, 5117, -1], 'generators': [25], 'label': '1152.155799.288.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '288.i1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968577
    {'ambient': '1152.155799', 'aut_centralizer_order': 256, 'aut_label': '288.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.o1.a1', '144.f1.a1', '144.m1.a1', '144.n1.a1', '144.v1.a1', '144.x1.a1', '144.ba1.a1', '144.bn1.a1'], 'contains': ['576.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7666, -1, 7144, -1, 3964, -1, 5180, -1], 'generators': [121], 'label': '1152.155799.288.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '288.j1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968578
    {'ambient': '1152.155799', 'aut_centralizer_order': 192, 'aut_label': '288.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.p1.a1', '96.t1.a1', '144.g1.a1', '144.p1.a1', '144.y1.a1', '144.bf1.a1', '144.bk1.a1', '144.bm1.a1', '144.bn1.a1'], 'contains': ['576.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8968, -1, 8815, -1, 5174, -1, 6692, -1], 'generators': [6], 'label': '1152.155799.288.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '288.k1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968579
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '288.l1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '72.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.q1.a1', '96.u1.a1', '96.w1.a1', '144.g1.a1', '144.t1.a1', '144.y1.a1', '144.bg1.a1', '144.bl1.a1', '144.bm1.a1', '144.bn1.a1'], 'contains': ['576.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8168, -1, 8327, -1, 5135, -1, 6637, -1], 'generators': [7], 'label': '1152.155799.288.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.e1.a1', 'old_label': '288.l1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968580
    {'ambient': '1152.155799', 'aut_centralizer_order': 2, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '576.8553', 'aut_weyl_index': 8, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '4.j1.a1'], 'contains': ['16.h1.a1', '16.j1.a1', '16.k1.a1', '24.cz1.a1', '24.dc1.a1', '24.dd1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4099, -1, 5393, -1, 8615, -1, 3758, -1], 'generators': [3, 384, 32, 12, 24, 48], 'label': '1152.155799.8.n1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '8.n1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1.a1', 'subgroup_fusion': None, 'weyl_group': '144.144'}
  • id: 60968581
    {'ambient': '1152.155799', 'aut_centralizer_order': 256, 'aut_label': '288.m1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.y1.a1', '144.c1.a1', '144.bo1.a1', '144.bp1.a1', '144.bq1.a1', '144.br1.a1'], 'contains': ['576.b1.a1', '576.c1.a1', '576.e1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1508, -1, 1405, -1, 1068, -1, 1504, -1], 'generators': [1, 96], 'label': '1152.155799.288.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '288.m1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60968582
    {'ambient': '1152.155799', 'aut_centralizer_order': 256, 'aut_label': '288.m1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.y1.b1', '144.c1.a1', '144.bo1.b1', '144.bp1.b1', '144.bq1.b1', '144.br1.b1'], 'contains': ['576.b1.b1', '576.c1.a1', '576.e1.b1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1508, -1, 1917, -1, 1068, -1, 1370, -1], 'generators': [49, 96], 'label': '1152.155799.288.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '288.m1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.m1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60968583
    {'ambient': '1152.155799', 'aut_centralizer_order': 256, 'aut_label': '288.n1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.z1.a1', '144.c1.a1', '144.bo1.a1', '144.bs1.a1', '144.bt1.a1'], 'contains': ['576.b1.a1', '576.d1.a1', '576.e1.b1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2921, -1, 3229, -1, 1626, -1, 2535, -1], 'generators': [1, 144], 'label': '1152.155799.288.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '288.n1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.n1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60968584
    {'ambient': '1152.155799', 'aut_centralizer_order': 256, 'aut_label': '288.n1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.z1.b1', '144.c1.a1', '144.bo1.b1', '144.bs1.b1', '144.bt1.b1'], 'contains': ['576.b1.b1', '576.d1.a1', '576.e1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2921, -1, 3309, -1, 1626, -1, 2570, -1], 'generators': [97, 144], 'label': '1152.155799.288.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '288.n1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.n1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60968585
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '288.o1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.x1.a1', '96.ba1.a1', '144.d1.a1', '144.bp1.a1', '144.bs1.a1'], 'contains': ['576.b1.a1', '576.f1.a1', '576.g1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1713, -1, 2030, -1, 1387, -1, 1574, -1], 'generators': [1, 2], 'label': '1152.155799.288.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.b1.a1', 'old_label': '288.o1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.o1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60968586
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '288.o1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.x1.b1', '96.ba1.b1', '144.d1.a1', '144.bp1.b1', '144.bs1.b1'], 'contains': ['576.b1.b1', '576.f1.a1', '576.g1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1713, -1, 2141, -1, 1387, -1, 1470, -1], 'generators': [49, 2], 'label': '1152.155799.288.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.b1.a1', 'old_label': '288.o1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.o1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60968587
    {'ambient': '1152.155799', 'aut_centralizer_order': 768, 'aut_label': '288.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bb1.a1', '144.a1.a1', '144.bo1.a1', '144.bo1.b1', '144.bu1.a1', '144.bv1.a1'], 'contains': ['576.c1.a1', '576.d1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1556, -1, 2074, -1, 1104, -1, 1539, -1], 'generators': [624, 96], 'label': '1152.155799.288.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '288.p1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.p1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968588
    {'ambient': '1152.155799', 'aut_centralizer_order': 128, 'aut_label': '288.q1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bc1.a1', '144.h1.a1', '144.bo1.b1', '144.br1.a1', '144.bw1.a1', '144.bx1.a1'], 'contains': ['576.c1.a1', '576.e1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1208, -1, 1838, -1, 1012, -1, 1435, -1], 'generators': [577, 96], 'label': '1152.155799.288.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '288.q1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.q1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968589
    {'ambient': '1152.155799', 'aut_centralizer_order': 128, 'aut_label': '288.q1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bc1.b1', '144.h1.a1', '144.bo1.a1', '144.br1.b1', '144.bw1.b1', '144.bx1.b1'], 'contains': ['576.c1.a1', '576.e1.b1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1208, -1, 1375, -1, 1012, -1, 1335, -1], 'generators': [625, 96], 'label': '1152.155799.288.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '288.q1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.q1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968590
    {'ambient': '1152.155799', 'aut_centralizer_order': 192, 'aut_label': '288.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '24.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bd1.a1', '144.i1.a1', '144.bp1.a1', '144.bp1.b1', '144.bu1.a1', '144.bw1.a1', '144.bw1.b1', '144.by1.a1'], 'contains': ['576.c1.a1', '576.f1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1383, -1, 1698, -1, 976, -1, 1273, -1], 'generators': [2, 576], 'label': '1152.155799.288.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '288.r1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.r1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968591
    {'ambient': '1152.155799', 'aut_centralizer_order': 2, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2304.oh', 'aut_weyl_index': 2, 'centralizer': '576.a1.a1', 'complements': ['576.b1.a1', '576.e1.a1', '576.b1.b1', '576.e1.b1', '576.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.e1.a1', '4.g1.a1', '6.q1.a1', '6.r1.a1', '8.l1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4222, 5408, 5256, 7501, 6362, 4798, 3817, 5387], 'generators': [13, 32, 384, 2, 48, 576, 672, 24], 'label': '1152.155799.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.e1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '576.8312', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': '576.8312'}
  • id: 60968592
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '144.183', 'aut_weyl_index': 32, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.b1.a1', '16.n1.a1', '16.o1.a1', '24.de1.a1', '24.dg1.a1', '32.i1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [281, -1, 258, -1, 424, -1, 382, -1], 'generators': [1, 576, 672, 2, 32, 384], 'label': '1152.155799.8.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.o1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.o1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 60968593
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '288.s1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.be1.a1', '144.j1.a1', '144.bp1.a1', '144.bp1.b1', '144.bv1.a1', '144.bx1.a1', '144.bx1.b1', '144.bz1.a1'], 'contains': ['576.c1.a1', '576.g1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1330, -1, 1489, -1, 940, -1, 1231, -1], 'generators': [3, 576], 'label': '1152.155799.288.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1.a1', 'old_label': '288.s1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.s1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968594
    {'ambient': '1152.155799', 'aut_centralizer_order': 192, 'aut_label': '288.t1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '24.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bf1.a1', '144.o1.a1', '144.bq1.a1', '144.bq1.b1', '144.bu1.a1', '144.bx1.a1', '144.bx1.b1', '144.by1.a1'], 'contains': ['576.c1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1104, -1, 1434, -1, 877, -1, 965, -1], 'generators': [98], 'label': '1152.155799.288.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '288.t1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.t1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968595
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '288.u1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bg1.a1', '144.s1.a1', '144.bq1.a1', '144.bq1.b1', '144.bv1.a1', '144.bw1.a1', '144.bw1.b1', '144.bz1.a1'], 'contains': ['576.c1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1132, -1, 1460, -1, 789, -1, 1060, -1], 'generators': [99], 'label': '1152.155799.288.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1.a1', 'old_label': '288.u1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.u1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968596
    {'ambient': '1152.155799', 'aut_centralizer_order': 128, 'aut_label': '288.v1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bi1.a1', '144.h1.a1', '144.bo1.a1', '144.bo1.b1'], 'contains': ['576.d1.a1', '576.e1.a1', '576.e1.b1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1827, -1, 2197, -1, 1558, -1, 1860, -1], 'generators': [577, 144], 'label': '1152.155799.288.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1.a1', 'old_label': '288.v1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.v1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60968597
    {'ambient': '1152.155799', 'aut_centralizer_order': 192, 'aut_label': '288.w1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '24.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bj1.a1', '144.i1.a1', '144.bs1.a1', '144.bs1.b1'], 'contains': ['576.d1.a1', '576.f1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2874, -1, 3153, -1, 1662, -1, 2501, -1], 'generators': [2, 624], 'label': '1152.155799.288.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.k1.a1', 'old_label': '288.w1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.w1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968598
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '288.x1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bk1.a1', '144.j1.a1', '144.bs1.a1', '144.bs1.b1'], 'contains': ['576.d1.a1', '576.g1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2808, -1, 3099, -1, 1522, -1, 2466, -1], 'generators': [3, 624], 'label': '1152.155799.288.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '288.x1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.x1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968599
    {'ambient': '1152.155799', 'aut_centralizer_order': 192, 'aut_label': '288.y1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '24.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bl1.a1', '144.q1.a1', '144.bt1.a1', '144.bt1.b1'], 'contains': ['576.d1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4325, -1, 4574, -1, 2842, -1, 4582, -1], 'generators': [582], 'label': '1152.155799.288.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.r1.a1', 'old_label': '288.y1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.y1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968600
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '288.z1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bm1.a1', '144.r1.a1', '144.bt1.a1', '144.bt1.b1'], 'contains': ['576.d1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4227, -1, 4500, -1, 2794, -1, 4535, -1], 'generators': [583], 'label': '1152.155799.288.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.i1.a1', 'old_label': '288.z1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.z1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968601
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '288.ba1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bn1.a1', '144.u1.a1', '144.bp1.a1', '144.bs1.b1'], 'contains': ['576.e1.a1', '576.f1.a1', '576.g1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2841, -1, 3198, -1, 1486, -1, 1765, -1], 'generators': [577, 2], 'label': '1152.155799.288.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.b1.a1', 'old_label': '288.ba1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60968602
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '288.ba1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bn1.b1', '144.u1.a1', '144.bp1.b1', '144.bs1.a1'], 'contains': ['576.e1.b1', '576.f1.a1', '576.g1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2841, -1, 2379, -1, 1486, -1, 1730, -1], 'generators': [625, 2], 'label': '1152.155799.288.ba1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.b1.a1', 'old_label': '288.ba1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ba1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60968603
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '144.183', 'aut_weyl_index': 32, 'centralizer': '576.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.b1.b1', '16.n1.a1', '16.o1.a1', '24.de1.b1', '24.dg1.b1', '32.i1.b1'], 'core': '16.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [281, -1, 329, -1, 424, -1, 252, -1], 'generators': [49, 576, 672, 2, 32, 384], 'label': '1152.155799.8.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.o1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.o1.b1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 60968604
    {'ambient': '1152.155799', 'aut_centralizer_order': 2304, 'aut_label': '384.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '2.d1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['128.a1.a1', '192.a1.a1', '192.b1.a1', '192.b1.b1', '192.f1.a1', '192.g1.a1', '192.h1.a1', '192.h1.b1', '192.i1.a1', '192.k1.a1'], 'contains': ['1152.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1879, 2471, 2297, 1967, 1355, 3866, 1698, 2582], 'generators': [384], 'label': '1152.155799.384.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '384.a1.a1', 'normal_contained_in': ['96.d1.a1', '192.a1.a1', '192.b1.b1', '192.b1.a1'], 'normal_contains': ['1152.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '384.a1.a1', 'projective_image': '1152.155799', 'quotient_action_image': '2.1', 'quotient_action_kernel': '192.960', 'quotient_action_kernel_order': 192, 'quotient_fusion': None, 'short_label': '384.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968605
    {'ambient': '1152.155799', 'aut_centralizer_order': 576, 'aut_label': '384.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.e1.a1', '128.a1.a1', '192.c1.a1', '192.e1.a1', '192.e1.b1', '192.j1.a1', '192.l1.a1'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [148, -1, 263, -1, 1258, -1, 547, -1], 'generators': [32], 'label': '1152.155799.384.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '384.b1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968606
    {'ambient': '1152.155799', 'aut_centralizer_order': 288, 'aut_label': '384.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2304, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bh1.a1', '128.a1.a1', '192.d1.a1', '192.m1.a1'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [671, -1, 843, -1, 1224, -1, 598, -1], 'generators': [416], 'label': '1152.155799.384.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.n1.a1', 'old_label': '384.c1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60968607
    {'ambient': '1152.155799', 'aut_centralizer_order': 4608, 'aut_label': '576.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1', '192.c1.a1', '192.d1.a1', '288.a1.a1', '288.c1.a1', '288.d1.a1', '288.e1.a1', '288.f1.a1', '288.g1.a1', '288.h1.a1', '288.i1.a1', '288.j1.a1', '288.k1.a1', '288.l1.a1'], 'contains': ['1152.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6989, 3586, 7116, 3575, 3508, 4361, 4024, 4470], 'generators': [48], 'label': '1152.155799.576.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '576.a1.a1', 'normal_contained_in': ['144.a1.a1', '192.a1.a1', '288.a1.a1'], 'normal_contains': ['1152.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '576.a1.a1', 'projective_image': '576.8312', 'quotient_action_image': '1.1', 'quotient_action_kernel': '576.8312', 'quotient_action_kernel_order': 576, 'quotient_fusion': None, 'short_label': '576.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60968608
    {'ambient': '1152.155799', 'aut_centralizer_order': 768, 'aut_label': '576.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.b1.a1', '192.e1.a1', '288.c1.a1', '288.m1.a1', '288.n1.a1', '288.o1.a1'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1803, -1, 2030, -1, 1387, -1, 1667, -1], 'generators': [1], 'label': '1152.155799.576.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '192.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '576.b1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60968609
    {'ambient': '1152.155799', 'aut_centralizer_order': 768, 'aut_label': '576.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.b1.b1', '192.e1.b1', '288.c1.a1', '288.m1.b1', '288.n1.b1', '288.o1.b1'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1803, -1, 2164, -1, 1387, -1, 1606, -1], 'generators': [49], 'label': '1152.155799.576.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '192.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '576.b1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60968610
    {'ambient': '1152.155799', 'aut_centralizer_order': 1536, 'aut_label': '576.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.f1.a1', '288.b1.a1', '288.d1.a1', '288.m1.a1', '288.m1.b1', '288.p1.a1', '288.q1.a1', '288.q1.b1', '288.r1.a1', '288.s1.a1', '288.t1.a1', '288.u1.a1'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1334, -1, 1511, -1, 976, -1, 1370, -1], 'generators': [96], 'label': '1152.155799.576.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '288.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '576.c1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60968611
    {'ambient': '1152.155799', 'aut_centralizer_order': 1536, 'aut_label': '576.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.g1.a1', '288.d1.a1', '288.n1.a1', '288.n1.b1', '288.p1.a1', '288.v1.a1', '288.w1.a1', '288.x1.a1', '288.y1.a1', '288.z1.a1'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2883, -1, 3229, -1, 1609, -1, 2535, -1], 'generators': [144], 'label': '1152.155799.576.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '576.d1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60968612
    {'ambient': '1152.155799', 'aut_centralizer_order': 256, 'aut_label': '576.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.h1.a1', '288.e1.a1', '288.m1.a1', '288.n1.b1', '288.q1.a1', '288.v1.a1', '288.ba1.a1'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1920, -1, 2337, -1, 1469, -1, 1796, -1], 'generators': [97], 'label': '1152.155799.576.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '576.e1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60968613
    {'ambient': '1152.155799', 'aut_centralizer_order': 256, 'aut_label': '576.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.h1.b1', '288.e1.a1', '288.m1.b1', '288.n1.a1', '288.q1.b1', '288.v1.a1', '288.ba1.b1'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1920, -1, 2211, -1, 1469, -1, 1763, -1], 'generators': [145], 'label': '1152.155799.576.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '576.e1.b1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60968614
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 36, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.b1.a1'], 'contains': ['18.a1.a1', '18.b1.a1', '18.c1.a1', '18.d1.a1', '18.e1.a1', '18.f1.a1', '18.g1.a1', '18.h1.a1', '18.i1.a1', '18.j1.a1', '18.k1.a1', '18.l1.a1', '18.m1.a1', '18.n1.a1', '18.o1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5858, -1, 6249, -1, 7209, -1, 7106, -1], 'generators': [1, 2, 12, 96], 'label': '1152.155799.9.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '576.8312', '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': '16.11'}
  • id: 60968615
    {'ambient': '1152.155799', 'aut_centralizer_order': 192, 'aut_label': '576.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '24.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.i1.a1', '192.j1.a1', '288.f1.a1', '288.o1.a1', '288.o1.b1', '288.r1.a1', '288.w1.a1', '288.ba1.a1', '288.ba1.b1'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1878, -1, 2279, -1, 1419, -1, 1637, -1], 'generators': [2], 'label': '1152.155799.576.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.j1.a1', 'old_label': '576.f1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60968616
    {'ambient': '1152.155799', 'aut_centralizer_order': 64, 'aut_label': '576.g1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.k1.a1', '192.l1.a1', '192.m1.a1', '288.g1.a1', '288.o1.a1', '288.o1.b1', '288.s1.a1', '288.x1.a1', '288.ba1.a1', '288.ba1.b1'], 'contains': ['1152.a1.a1'], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1661, -1, 2121, -1, 1323, -1, 1576, -1], 'generators': [3], 'label': '1152.155799.576.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.b1.a1', 'old_label': '576.g1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60968617
    {'ambient': '1152.155799', 'aut_centralizer_order': None, 'aut_label': '1152.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': ['384.a1.a1', '384.b1.a1', '384.c1.a1', '576.a1.a1', '576.b1.a1', '576.b1.b1', '576.c1.a1', '576.d1.a1', '576.e1.a1', '576.e1.b1', '576.f1.a1', '576.g1.a1'], 'contains': [], 'core': '1152.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1814, 2471, 2177, 2572, 1371, 3866, 1652, 4162], 'generators': [], 'label': '1152.155799.1152.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1152.a1.a1', 'normal_contained_in': ['288.b1.a1', '384.a1.a1', '576.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1152.a1.a1', 'projective_image': '1152.155799', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60968618
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '144.192', 'aut_weyl_index': 32, 'centralizer': '36.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.j1.a1', '6.k1.a1'], 'contains': ['24.a1.a1', '24.c1.a1', '24.d1.a1', '24.k1.a1', '24.l1.a1', '24.w1.a1', '24.x1.a1', '36.k1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3927, 5658, 4542, 3952, 3906, 5807, 5003, 3420], 'generators': [1, 384, 48, 24, 96, 576], 'label': '1152.155799.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '24.c1.a1', '24.d1.a1', '48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '576.8312', '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': '36.10'}
  • id: 60968619
    {'ambient': '1152.155799', 'aut_centralizer_order': 24, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.b1.a1', '6.c1.a1', '6.r1.a1'], 'contains': ['24.e1.a1', '24.bz1.a1', '36.bn1.a1', '48.bl1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3051, 4543, 3407, 8528, 5137, 4772, 3291, 7816], 'generators': [2, 576, 672, 24, 48, 32], 'label': '1152.155799.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.b1.a1', '6.b1.a1'], 'normal_contains': ['24.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '576.8312', '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': '96.187'}
  • id: 60968620
    {'ambient': '1152.155799', 'aut_centralizer_order': 96, 'aut_label': '12.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '12.c1.a1', 'complements': ['96.x1.a1', '96.x1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.a1.a1', '6.p1.a1', '6.t1.a1'], 'contains': ['24.c1.a1', '24.bn1.a1', '24.bo1.a1', '36.a1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5660, 9338, 6655, 7106, 6546, 9219, 7171, 6580], 'generators': [12, 48, 24, 96, 576, 384], 'label': '1152.155799.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.f1.a1', '6.a1.a1'], 'normal_contains': ['24.c1.a1', '36.a1.a1', '48.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '576.8312', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968621
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '12.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '144.192', 'aut_weyl_index': 32, 'centralizer': '36.a1.a1', 'complements': ['96.x1.a1', '96.x1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.a1.a1', '6.q1.a1', '6.s1.a1'], 'contains': ['24.c1.a1', '24.bp1.a1', '24.bq1.a1', '36.br1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6203, 8050, 6558, 5485, 7208, 8024, 7843, 4735], 'generators': [13, 384, 48, 96, 576, 24], 'label': '1152.155799.12.d1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.d1.a1', 'normal_contained_in': ['4.g1.a1', '6.a1.a1'], 'normal_contains': ['24.c1.a1', '48.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '576.8312', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 60968622
    {'ambient': '1152.155799', 'aut_centralizer_order': 24, 'aut_label': '12.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': ['96.ba1.a1', '96.bn1.a1', '96.ba1.b1', '96.bn1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.b1.a1', '6.d1.a1', '6.u1.a1'], 'contains': ['24.e1.a1', '24.cg1.a1', '36.bp1.a1', '48.by1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3088, 3905, 4761, 7960, 5820, 4181, 3578, 7312], 'generators': [6, 576, 96, 24, 48, 32], 'label': '1152.155799.12.e1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.e1.a1', 'normal_contained_in': ['4.d1.a1', '6.b1.a1'], 'normal_contains': ['24.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '576.8312', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '96.187'}
  • id: 60968623
    {'ambient': '1152.155799', 'aut_centralizer_order': 48, 'aut_label': '12.f1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '24.b1.a1', 'complements': ['96.ba1.a1', '96.bn1.a1', '96.ba1.b1', '96.bn1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.b1.a1', '6.e1.a1', '6.v1.a1'], 'contains': ['24.e1.a1', '36.a1.a1', '48.ca1.a1'], 'core': '12.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4584, 6926, 5731, 9227, 9038, 6983, 4207, 8547], 'generators': [12, 576, 96, 32, 24, 48], 'label': '1152.155799.12.f1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.f1.a1', 'normal_contained_in': ['4.f1.a1', '6.b1.a1'], 'normal_contains': ['24.e1.a1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '576.8312', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60968624
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.c1.a1'], 'contains': ['24.f1.a1', '24.bz1.a1', '24.cb1.a1', '24.de1.a1', '24.de1.b1', '36.j1.a1', '48.g1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1029, -1, 861, -1, 1553, -1, 1348, -1], 'generators': [1, 576, 672, 2, 48, 32], 'label': '1152.155799.12.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.g1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 60968625
    {'ambient': '1152.155799', 'aut_centralizer_order': 2, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2304.oh', 'aut_weyl_index': 2, 'centralizer': '576.a1.a1', 'complements': ['576.f1.a1', '576.b1.a1', '576.e1.a1', '576.b1.b1', '576.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.d1.a1', '4.g1.a1', '6.s1.a1', '6.u1.a1', '8.m1.a1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4282, 3531, 5497, 5548, 6428, 3834, 4003, 6182], 'generators': [13, 32, 384, 6, 48, 576, 96, 24], 'label': '1152.155799.2.f1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.d1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': '576.8312', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.f1.a1', 'subgroup_fusion': None, 'weyl_group': '576.8312'}
  • id: 60968626
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '72.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.c1.a1', '6.d1.a1', '6.e1.a1'], 'contains': ['24.e1.a1', '24.f1.a1', '24.cf1.a1', '36.k1.a1', '48.h1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2163, -1, 3193, -1, 4186, -1, 2824, -1], 'generators': [1, 576, 96, 24, 32, 48], 'label': '1152.155799.12.h1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.h1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 60968627
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.226', 'aut_weyl_index': 48, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.d1.a1'], 'contains': ['24.f1.a1', '24.cg1.a1', '24.ch1.a1', '36.l1.a1', '48.i1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1498, -1, 1918, -1, 3428, -1, 2989, -1], 'generators': [1, 576, 96, 6, 48, 32], 'label': '1152.155799.12.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.i1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 60968628
    {'ambient': '1152.155799', 'aut_centralizer_order': 2, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '4.j1.a1'], 'contains': ['24.g1.a1', '24.h1.a1', '24.i1.a1', '24.cv1.a1', '24.cw1.a1', '24.db1.a1', '24.dc1.a1', '36.m1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3420, -1, 4630, -1, 9631, -1, 3681, -1], 'generators': [1, 32, 48, 2, 12, 24], 'label': '1152.155799.12.j1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '12.j1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
  • id: 60968629
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 24, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.a1'], 'contains': ['24.j1.a1', '24.l1.a1', '24.m1.a1', '24.bb1.a1', '24.bc1.a1', '24.be1.a1', '24.bf1.a1', '36.b1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3267, -1, 3738, -1, 2072, -1, 2534, -1], 'generators': [1, 384, 576, 2, 120, 624], 'label': '1152.155799.12.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '12.k1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60968630
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.g1.a1', '6.j1.a1'], 'contains': ['24.j1.a1', '24.k1.a1', '24.p1.a1', '24.q1.a1', '24.ba1.a1', '24.bd1.a1', '24.bg1.a1', '24.ck1.a1', '24.cl1.a1', '36.c1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7172, -1, 7326, -1, 4667, -1, 5644, -1], 'generators': [1, 384, 48, 2, 24, 576], 'label': '1152.155799.12.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.l1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968631
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '6.i1.a1', '6.j1.a1'], 'contains': ['24.k1.a1', '24.m1.a1', '24.bh1.a1', '24.bl1.a1', '24.bt1.a1', '36.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5970, -1, 6111, -1, 4269, -1, 5474, -1], 'generators': [1, 384, 576, 98, 24, 48], 'label': '1152.155799.12.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.m1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968632
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.h1.a1', '6.k1.a1'], 'contains': ['24.k1.a1', '24.n1.a1', '24.r1.a1', '24.t1.a1', '24.bi1.a1', '24.bm1.a1', '24.bu1.a1', '24.cm1.a1', '24.cq1.a1', '36.e1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8750, -1, 8617, -1, 5370, -1, 7759, -1], 'generators': [1, 384, 48, 6, 24, 96], 'label': '1152.155799.12.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.n1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968633
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '6.i1.a1', '6.k1.a1'], 'contains': ['24.k1.a1', '24.o1.a1', '24.bj1.a1', '24.bk1.a1', '24.bv1.a1', '36.f1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6037, -1, 6296, -1, 4750, -1, 5789, -1], 'generators': [1, 384, 96, 582, 24, 144], 'label': '1152.155799.12.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.o1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968634
    {'ambient': '1152.155799', 'aut_centralizer_order': 32, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 96, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.f1.a1', '6.i1.a1'], 'contains': ['24.b1.a1', '24.k1.a1', '24.s1.a1', '24.bn1.a1', '24.bp1.a1', '24.cn1.a1', '24.co1.a1', '36.g1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7758, -1, 8914, -1, 8428, -1, 9129, -1], 'generators': [1, 384, 48, 12, 96, 24], 'label': '1152.155799.12.p1.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': '12.p1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.p1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968635
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '12.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.g1.a1', '6.h1.a1'], 'contains': ['24.k1.a1', '24.s1.a1', '24.bo1.a1', '24.bq1.a1', '24.cp1.a1', '36.h1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8086, -1, 8992, -1, 6941, -1, 8751, -1], 'generators': [1, 384, 48, 588, 96, 24], 'label': '1152.155799.12.q1.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': '12.q1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.q1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968636
    {'ambient': '1152.155799', 'aut_centralizer_order': 2, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2304.oh', 'aut_weyl_index': 2, 'centralizer': '576.a1.a1', 'complements': ['576.f1.a1', '576.b1.a1', '576.e1.a1', '576.b1.b1', '576.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.e1.a1', '4.f1.a1', '6.t1.a1', '6.v1.a1', '6.w1.a1', '8.n1.a1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4150, 4377, 5393, 8423, 5946, 3050, 3754, 7704], 'generators': [3, 32, 384, 12, 48, 576, 672, 24], 'label': '1152.155799.2.g1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.e1.a1', '4.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.a1', 'projective_image': '576.8312', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.g1.a1', 'subgroup_fusion': None, 'weyl_group': '576.8312'}
  • id: 60968637
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 24, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1.a1'], 'contains': ['24.l1.a1', '24.n1.a1', '24.o1.a1', '24.br1.a1', '24.bs1.a1', '24.bw1.a1', '24.bx1.a1', '36.i1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4900, -1, 4928, -1, 3310, -1, 5351, -1], 'generators': [1, 384, 96, 6, 600, 48], 'label': '1152.155799.12.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '12.r1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.r1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60968638
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '12.s1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.j1.a1'], 'contains': ['24.a1.a1', '24.j1.a1', '24.m1.a1', '24.u1.a1', '24.v1.a1', '24.by1.a1', '24.ca1.a1', '24.df1.a1', '24.df1.b1', '24.dg1.a1', '24.dg1.b1', '36.j1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1589, -1, 2016, -1, 1262, -1, 1728, -1], 'generators': [1, 384, 576, 2, 48, 96], 'label': '1152.155799.12.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '12.s1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.s1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60968639
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '12.t1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.k1.a1'], 'contains': ['24.a1.a1', '24.n1.a1', '24.o1.a1', '24.y1.a1', '24.z1.a1', '24.cd1.a1', '24.ce1.a1', '36.l1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3504, -1, 4248, -1, 3039, -1, 4702, -1], 'generators': [1, 384, 96, 6, 576, 48], 'label': '1152.155799.12.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '12.t1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.t1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60968640
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '12.u1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '6.f1.a1'], 'contains': ['24.b1.a1', '24.p1.a1', '24.r1.a1', '24.cr1.a1', '24.ct1.a1', '24.cx1.a1', '24.cz1.a1', '36.m1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6895, -1, 8293, -1, 8926, -1, 8239, -1], 'generators': [1, 384, 48, 2, 12, 24], 'label': '1152.155799.12.u1.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.u1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.u1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60968641
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '12.v1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1'], 'contains': ['24.p1.a1', '24.r1.a1', '24.s1.a1', '24.cs1.a1', '24.cu1.a1', '24.cy1.a1', '24.da1.a1', '36.n1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9382, -1, 9414, -1, 8333, -1, 9326, -1], 'generators': [1, 384, 48, 2, 588, 24], 'label': '1152.155799.12.v1.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': '12.v1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.v1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 60968642
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '12.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 24, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.a1'], 'contains': ['24.u1.a1', '24.v1.a1', '24.x1.a1', '24.ba1.a1', '24.bb1.a1', '24.be1.a1', '24.bt1.a1', '36.o1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3206, -1, 3681, -1, 1947, -1, 2469, -1], 'generators': [97, 384, 576, 2, 120, 624], 'label': '1152.155799.12.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '12.w1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.w1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60968643
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.a1', '6.l1.a1', '6.m1.a1'], 'contains': ['24.u1.a1', '24.w1.a1', '24.bc1.a1', '24.bd1.a1', '24.bl1.a1', '36.p1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7233, -1, 6897, -1, 4449, -1, 5580, -1], 'generators': [97, 384, 576, 2, 24, 48], 'label': '1152.155799.12.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.x1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968644
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '12.y1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.a1', '6.n1.a1', '6.o1.a1'], 'contains': ['24.v1.a1', '24.w1.a1', '24.bf1.a1', '24.bg1.a1', '24.bh1.a1', '36.q1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6295, -1, 7648, -1, 4813, -1, 5535, -1], 'generators': [97, 384, 576, 98, 24, 48], 'label': '1152.155799.12.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.y1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.y1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968645
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '12.z1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1.a1', '6.l1.a1', '6.n1.a1'], 'contains': ['24.w1.a1', '24.y1.a1', '24.bi1.a1', '24.bk1.a1', '24.bw1.a1', '36.r1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7468, -1, 6947, -1, 5078, -1, 6021, -1], 'generators': [577, 384, 96, 6, 24, 48], 'label': '1152.155799.12.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.z1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.z1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968646
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '12.ba1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1.a1', '6.m1.a1', '6.o1.a1'], 'contains': ['24.w1.a1', '24.z1.a1', '24.bj1.a1', '24.bm1.a1', '24.bx1.a1', '36.s1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6347, -1, 7452, -1, 4956, -1, 6084, -1], 'generators': [577, 384, 96, 582, 24, 144], 'label': '1152.155799.12.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.ba1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968647
    {'ambient': '1152.155799', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '768.1090146', 'aut_weyl_index': 6, 'centralizer': '288.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.a1', '6.c1.a1', '6.d1.a1', '6.e1.a1', '6.r1.a1', '6.u1.a1', '6.v1.a1', '9.a1.a1', '12.j1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3655, -1, 4620, -1, 7303, -1, 3676, -1], 'generators': [1, 48, 32, 2, 24, 576, 672, 12], 'label': '1152.155799.3.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.187'}
  • id: 60968648
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '12.bb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.l1.a1', '6.o1.a1'], 'contains': ['24.w1.a1', '24.bn1.a1', '24.bq1.a1', '24.cn1.a1', '24.cp1.a1', '36.t1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7842, -1, 8695, -1, 7815, -1, 8574, -1], 'generators': [577, 384, 48, 12, 96, 24], 'label': '1152.155799.12.bb1.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': '12.bb1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968649
    {'ambient': '1152.155799', 'aut_centralizer_order': 16, 'aut_label': '12.bc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 48, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.m1.a1', '6.n1.a1'], 'contains': ['24.w1.a1', '24.bo1.a1', '24.bp1.a1', '24.co1.a1', '24.cp1.a1', '36.u1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8388, -1, 8835, -1, 7120, -1, 8663, -1], 'generators': [577, 384, 48, 588, 96, 24], 'label': '1152.155799.12.bc1.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': '12.bc1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60968650
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '12.bd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 24, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1.a1'], 'contains': ['24.x1.a1', '24.y1.a1', '24.z1.a1', '24.br1.a1', '24.bs1.a1', '24.bu1.a1', '24.bv1.a1', '36.v1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4765, -1, 4880, -1, 3253, -1, 5406, -1], 'generators': [577, 384, 96, 6, 600, 48], 'label': '1152.155799.12.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '12.bd1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 60968651
    {'ambient': '1152.155799', 'aut_centralizer_order': 24, 'aut_label': '12.be1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 72, 'centralizer': '96.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.l1.a1', '6.p1.a1'], 'contains': ['24.bd1.a1', '24.bi1.a1', '24.bn1.a1', '24.cr1.a1', '24.cs1.a1', '36.w1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8540, -1, 7166, -1, 8167, -1, 8146, -1], 'generators': [2, 48, 24, 12, 576, 384], 'label': '1152.155799.12.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.be1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.be1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60968652
    {'ambient': '1152.155799', 'aut_centralizer_order': 12, 'aut_label': '12.bf1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 36, 'centralizer': '96.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '6.m1.a1', '6.p1.a1'], 'contains': ['24.bd1.a1', '24.bj1.a1', '24.bo1.a1', '36.x1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7385, -1, 7581, -1, 6014, -1, 6929, -1], 'generators': [2, 48, 576, 108, 384, 600], 'label': '1152.155799.12.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bf1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 60968653
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '12.bg1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '6.l1.a1', '6.q1.a1'], 'contains': ['24.bd1.a1', '24.bk1.a1', '24.bq1.a1', '36.y1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7286, -1, 7013, -1, 5880, -1, 6448, -1], 'generators': [109, 384, 48, 2, 24, 576], 'label': '1152.155799.12.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bg1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968654
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '12.bh1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.m1.a1', '6.q1.a1'], 'contains': ['24.bd1.a1', '24.bm1.a1', '24.bp1.a1', '24.ct1.a1', '24.cu1.a1', '36.z1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7994, -1, 8393, -1, 7990, -1, 8339, -1], 'generators': [13, 384, 48, 2, 576, 24], 'label': '1152.155799.12.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bh1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968655
    {'ambient': '1152.155799', 'aut_centralizer_order': 8, 'aut_label': '12.bi1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 24, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.n1.a1', '6.s1.a1'], 'contains': ['24.bg1.a1', '24.bi1.a1', '24.bp1.a1', '24.cx1.a1', '24.cy1.a1', '36.ba1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8675, -1, 8471, -1, 8082, -1, 8428, -1], 'generators': [13, 384, 48, 6, 96, 24], 'label': '1152.155799.12.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bi1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968656
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '12.bj1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '6.o1.a1', '6.s1.a1'], 'contains': ['24.bg1.a1', '24.bj1.a1', '24.bq1.a1', '36.bb1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6684, -1, 7390, -1, 6343, -1, 6585, -1], 'generators': [589, 384, 48, 582, 24, 96], 'label': '1152.155799.12.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bj1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 60968657
    {'ambient': '1152.155799', 'aut_centralizer_order': 4, 'aut_label': '12.bk1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 12, 'centralizer': '288.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '6.n1.a1', '6.t1.a1'], 'contains': ['24.bg1.a1', '24.bk1.a1', '24.bo1.a1', '36.bc1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7090, -1, 7512, -1, 5625, -1, 6311, -1], 'generators': [3, 384, 48, 108, 600, 576], 'label': '1152.155799.12.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bk1.a1', 'projective_image': '576.8312', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}